Differentiation Definition and 1000 Threads

I was working through this problem, I understand the method, but got stuck trying to differentiate the arc tan terms... In the table of standard derivatives, \frac{d}{dx} \arctan{x} = \frac{1}{1+x^2} and for PDE's, you treat y as constant when differentiating w.r.t. x --- Any...

Homework Statement "An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to each other. One plane is 120 miles from the point and is moving at 400 miles per hour. The other plane is 160 miles from the point and has a speed of...

find derivative of y=(sqrt(8x^4-5))/ (x-1) ok...after working out the tricky calculations i get for my final answer: (32x^4sqrt(8x^4-5)-64x^3sqrt(8x^4-5)) / (16x^6-32x^5+ 16x^4-10x^2+20x-10) I don't know if you want to do the math...im just wondering if i can simplify it anymore. thanks

A Norman window has the shape of a square surmounted by a semicircle. The base of the window is measured as having 80cm with a possible error in measurement of 0.1cm. Use differentials to estimate the maximum possible error in computing the area of the window. So what i did was...

Homework Statement I'm having trouble deriving the following equation \frac {\partial^2 {\theta}}{\partial {x'^2}} = -y^2*exp(\theta) and y = x/x' my main problem is the exponent Homework Equations The Attempt at a Solution Normally i would use the equation (x')'' + k^2*x' = 0 x' = c1...

Homework Statement If f'x = 0 \forall x \in (a,b), show that f is constant there. I've gotten a final result, but I'm not entirely sure if I actually showed what I intended to show... Homework Equations The Attempt at a Solution Fix a point c \in (a,b) and choose a point x...

The tangent to the curve y=ax^3 at the point (-1,b) is perpendicular to the line y = 2x+3. Find the values of a and b. Could someone show me how to answer that?

Homework Statement Differentiate f(x) if f(x)=xxln(3x-6) Homework Equations None The Attempt at a Solution The problem in f(x) is the xx so what I did was let a=xx and differentiated a with respect to x. I ended up with da/dx= (ln(x)+1)xx. Afterwards, I modified f(x) by...

Okay, so my problem lies within taking the second derivative of a change of variable equation. w = f(x,y); x = u + v, y = u - v so far I have the first derivative: dw/dx = (dw/dv)(dv/dx) + (dw/du)(du/dx) = (d/dv + d/du)w Now I'm having problems in finding my second derivative...

Homework Statement Find all the points on the curve x^{2}y^{2}+xy=2 where the slope of the tangent line is -1. The Attempt at a Solution I differentiated both sides of the equation and got: \frac{dy}{dx}=\frac{-2xy^{2}-y}{x^{2}2y+x} I know that \frac{dy}{dx}=-1, but if I substitute...

Homework Statement i have been told to calculate DI/Dx i calculated I as being = m(L^2)/16 how do i differentiate this? I am confussed with what happens to the m is it a constant an just removed? same with the 1/16 i assume that is removed as a constant? just need some clarification...

Homework Statement Given the equation y= f(x) , at a certain point the slope of the curve is 1/2 and the x-coordinate decreases at 3 units/s. At that point, how fast is the y-coordinate of the object changing? The Attempt at a Solution Dy/dx = f ' (x) dx/dt Would that be...

Homework Statement f(x) = (2x-1)(3x-2)(5x+1) d/dx = ? Note that I am letting (2x-1)(3x-2) = f and 5x+1 = g Homework Equations d/dx (fg) = f d/dx g + g d/dx f The Attempt at a Solution d/dx y = (2x-1)(3x-2)d/dx(5x+1)+(5x+1)d/dx((2x-1)(3x-2)) = (2x-1)(3x-2)(5)+...

Homework Statement (x^(3)+2x) / (x^(2)-5) d/dx = ? Homework Equations d/dx (f/g) = (g d/dx (f) - f d/dx (g)) / g^2 The Attempt at a Solution d/dx y = { (x^(2)-5) d/dx (x^(3)+2x) - (x^(3)+2x) d/dx (x^(2)-5) } / (x^(2)-5)^2 This is where it gets complicated for me. {...

Homework Statement Find the slope of the curve y=\frac{x}{3x+2} at the point x = -2. Homework Equations \lim_{h \rightarrow 0}\frac{f(x_{0} + h) - f(x_{0})}{h} = m The Attempt at a Solution If x = -2, then y = 1/2. I'm not sure what to do from here. This is the first step, but I don't get...

Homework Statement Consider: x^3+y^3+2xy=4, y=1 when x=1 a.) Find the equation of the tangent line to the curve when x=1. b.) Find y'' at x=1. c.) Is the graph of y=f(x) concave up or concave down near x=1? Homework Equations Any derivative rules... The Attempt at a Solution For Part a...

Homework Statement y = x^(18x^-4) Homework Equations chain rule dy/dx a^x = a^x ln a The Attempt at a Solution first i used the second equation from above to get x^(18/x^4)*ln(x) then i use the chain rule to get x^(18/x^4)*ln(x)*(-72x^-5) the computer program i am using is...

Alright, I'm not technically stuck on this one, but I consistently get a result that disagrees with what Wolfram Alpha shows when I enter the problem to check my answer. Sorry 'bout the lack of LaTeX, but it should be simple enough to read. Here goes: Problem: Differentiate y=sin-1[x/(1+x)]...

Homework Statement Suppose f(3)=2 , f'(3)=5 , and f''(3)= -2 . Then d²/dx² (f²(x)) at x=3 is equal to ____? A. -20 B. 20 C. 38 D. 42 E. 10 The Attempt at a Solution I am confused about how to find the function to get the derivative from that function. Any Ideas? Thanks.

Find d^2/dx^2(3y^2+8y=3x) I managed to get dy/dx = 3 / (6y + 8) but I have no clue where to go from here. According to WolfRamAlpha, the answer is -27/(4(16 + 9x)(4 + 3y)), but since dy/dx doesn't have any x value in it, I don't see how the derivative of it would. I've played around...

Homework Statement Find y´(x) for x + y = 1/x^2 + 8/y^2 Homework Equations The Attempt at a Solution Rewrite the eq. as x + y = x^-2 + 8y^-2 differentiate. 1 + y´(x) = (-2x^-3) + (-16y^-3)(y´(x)) Rearrange 1 + (2x^-3) = (-16y^-3)(y´(x)) - (y´(x)) (1 + (2x^-3))/(16y^-3) =...

1. Suppose the curve f(x)=(x^4)+a(x^3)+b(x^2)+cx+d has tangent line when x=0 with equation y=2x+1, and a tangent line when x=1 with equation y=2-3x. Find a,b,c,d 2. d/dx f(x)g(x)=g*f`+f*g` 3. f`(x)=4x^3+3ax^2+2bx+c x=0 y=2x+1 y=1 (0,1) is a point on f(x) x=1 y=2x-3 y=-1 (1,-1) is a point on...

Homework Statement If g(x) + x sin g(x) = x^2 find g'(0) Homework Equations The Attempt at a Solution At this point I have tried a few things but hit deadends. Any help would be appreciated.

Homework Statement Having trouble understanding this the example I saw was; Solve \int^{\infty}_{0} x^3 e^{-9x} dx using integration by parametric differentiation.The Attempt at a Solution well, i do know how to do this, so i set out my integral; \int^{\infty}_{0} e^{-\alpha x} dx =...

Homework Statement Find y'' by implicit differentiation. Homework Equations The Attempt at a Solution I get to this point in the problem, which is I solved for y'. But then when I attempt to take y'', in other words take the derivative of my answer for y', I...

2xy=3x-y^2 find dy/dx and d2y/dx2 I just want to make sure my answer is right and simplified I got dy/dx= (3-2y)/ (2x+2y) Now d2y/dx2 took some time but this is what i got: (-12x+2x2y+9+4yx-14y-4y^2) / ((x+y)(2x+2y)^2)

I guess the following identity isn't right. Can anyone tell me what the LHS is really equal to? \frac{\partial}{\partial x}\int_{-\infty}^\infty\int_0^x f(s,t) dsdt = \int_{-\infty}^\infty f(x,t)dt

1. use implicit differentiation to evaluate y(prime) for x^3+y^3=4xy+1 at the point (2,1)

so to solve this i differentiated each part and got 6dy/dx + 8 = cos(xy^2)(y^2*x2ydy/dx) then i divided both sides by cos(xy^2) then serpatated the 6dy/dx + 8 and put them both over cos(xy^2) then i took out a yprime and ended up with -8/(6-2y^3xcos(xy^2)) as an answer but its wrong...

Homework Statement The function f is defined as f(x)=x^4, then; f'(3x^3)=? d[f(3x^3)]/dx=? f'(xy^3)=? Homework Equations The Attempt at a Solution My problem here is not so much doing the differentiation itself but understanding the notation. 1. for f'(3x^3) i want...

some help with this differentiation question thanks Question : Find the indicated partial derivative . frss , frst f(r,s,t) = r ln (rs^2t^3) differentiating with respect to r gave s^2t^3 1* ---------- rs^2 t^3 but this is not correct something is...

Hi all, I was reading a paper in which implicit differentiation was used as follows x \in R, \lambda \in R Given G(x,\lambda) = 0 \frac{\partial G(x,\lambda)}{\partial x} \frac{\partial x}{\partial \lambda} + \frac{\partial G(x,\lambda)}{\partial \lambda} = 0 My doubt is...

Hi, So, I am reviewing Cal III, and I have come across something that I do not understand regarding implicit differentiation with partial derivatives: x^3 + y^3 + z^3 + 6xyz = 1 implicit differentiation of z with respect to x: 3x^2 + 3z^2(dz/dx) + 6yz + 6xy(dz/dx) = 0 *notive the...

Homework Statement Prove if f(x) is differentiable at x=a then f'(a)=lim_{h\rightarrow0}\frac{f(a+h)-f(a-h)}{2h}Homework Equations I know that the derivative is defined as f'(a)=lim_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}The Attempt at a Solution Starting from the definition I used a known...

Homework Statement The function f(x,y) satisfies the d.e. y{\partial f \over \partial x} + x{\partial f \over \partial y} = 0 By changing to new vars u = x^2-y^2 and v=2xy show that f is a function of x^2-y^2 only. Homework Equations \frac{\partial }{\partial x}=\frac{\partial...

Homework Statement Use implicit differentiation to find ∂z/∂x and ∂z/∂y yz = ln(x + z) The Attempt at a Solution I came up with (x+2)/(x+2)(1-xy-yz) Could someone please help me solve this. I know to treat y as a constant and to multiply all the derivatives of z by ∂z/∂x

Hi There, I'm currently using the definition of exponential functions: e^z=(e^x)(e^iy) I need help defining: sin(z)=(e^(iz)-e(-iz))/(2i) cos(z)=(e^(iz)+e(-iz))/(2) And showing that sin'(z) = cos(z) cos'(z) = -sin(z) (sin(z))^2+(cos(z))^2=1 Any help would be appreciated...

I'm having trouble understanding where this concept comes from: Step 1) If you start out with the following two equations v + log u = xy u + log v = x - y. Step 2) And then perform implicit differentiation, taking v and u to be dependent upon both x and y: (d will represent the partial...

Homework Statement This is the larger problem to the small portion that I already posted in the Precalc Hw help forum. I still can't figure out how to get to the answer. The problem is this: I am trying to find the derivative of f(x)=x+\frac{9}{x}. Homework Equations I know via power...

Homework Statement 2*y + sin(y) = x^4 + 4(x)^3 + (2(Pi) - 5), show that dy/dx = 16, when x = 1. Homework Equations The Attempt at a Solution So I implicitly differentiated it to be dy/dx(2 + cos(y)) = 4(x)^3 + 12(x)^2, and I end up with dy/dx = 16 / (2 + cos (y)) which means that...

Homework Statement Assume that the following equation define the implicit function y=(x). Find the its derivative: x2 + 2xy - y2 = a2 y'=? y''=? Homework Equations \frac{dy}{dx} = -\frac{F_x}{F_y} The Attempt at a Solution so for the first derivative I express that equation as...

Differentiation of damped motion function - Need help urgently! Homework Statement Basically my task was to come up with a function to model the swing of a pendulum. The model I came up with was: 0.16e^{-0.25t}cos((\stackrel{2\pi}{1.22})t-0.8) + 0.814 The next part of my task asks me...

Hi, I am working on my differential equations excercises and I encountered 2 problems. First one is, I just wanted to check if I did this implicit differenriation right Homework Statement t^{2} \bullet y +y^{2} = C where is is a constant The Attempt at a Solution My solution is y...

Hi, I've got the following problem: Show that if z = x^nf(u) and u = y/x then x\frac{\partial{z}}{\partial{x}} + y\frac{\partial{z}}{\partial{y}} = nz I know partial differentiation fairly well, but I've never seen one laid out like this before, and am not too sure how to get started...

In one of my electronics textbooks I have the following equation related to feedback in amplifiers: K_f = \frac{K}{1-K\beta} \frac{dK_f}{K_f} = \frac{1}{1-K\beta}\frac{dK}{K} I'm not sure how this was derived - how was Kf differentiated with respect to itself?

Differentiate with respect to x; (using the quotient rule) 3/2x-1 (3 over 2x minus 1) dy/dx = (2x-1)(0) - (3)(2) / (2x-1)^2 dy/dx = -6/(2x-1)^2 but my book gives -2/(2x-1)^2 now, y = u/v and i take u = 3 and v = 2x-1. dy/dx = v(du/dx) -...

I am very interested in math and I find calculus to be a particularly interesting subject, but one major problem I have with it is that I cannot find a consistent explanation of the rules of differentials (infantesimals) that explains all the things mathematicians do with them. I have truly...

Homework Statement By using cos and sin subs for tan and sec, find the gradient of: ln(tan2x+secx) Homework Equations tanx=sinx/cosx secx=1/cosx The Attempt at a Solution Substituting y=ln(\frac{sin2x}{cos2x}+\frac{1}{cosx}) Using the chain rule let: z=...

Homework Statement Find where; f(z) = (z+1)/(z-i) is differentiable on the complex plane and find the formulas for f' Homework Equations CR equations; if f(z) = u(x,y) + iv(x,y) u_x - v_y = 0 v_x + u_y = 0 if function is differentiable The Attempt at a Solution...

Differentiation problem and finding maximum, need helping :)? have a few problems with these questions, can you help :) Using differentiation, find the MAXIMUM value of the following functions? 1. f(x) = x2 / 4 + 4 / x 2. f(x) = xe-2x2 3. f(x) = sqrt(x - n) / x ; n>0 hope you guys...