Differentiation Definition and 1000 Threads

Homework Statement 1. Calculate the gradient of the curve y = 2x3 - 5x2 + 46x + 87 at the point where it crosses the x-axix. 2. Show by differentiation and solving a quadratic equation, that there are no points on the above curve where the gradient is zero.Homework Equations y = 2x3 - 5x2 +...

Homework Statement Consider y = 2a + ax find dy/dx dy/dx = a That is right is it not, as a is treated merly as a constantNow consider this question: Use the substitution y = vx to transform the equation: dy/dx = (4x+y)(x+y)/x² into x(dv/dx) = (2+v)² According to the mark scheme they...

i am given two differentiable function f and g . prove that for u(x)=max(f(x),g(x)) and v(x)=min(f(x),g(x)) there is one sided derivatives ??how to put mim ,max functions into the formula of derivative formula?? f'(x)_+ = \lim_{h \to 0^+} \frac {f(x + h) - f(x)}h (one-sided derivative...from...

Homework Statement Use logarithmic differentiation to find the derivative of the function. Homework Equations y = (sin(x))^(ln(x)) The Attempt at a Solution I guessing the first step is raise both sides to "e", but so far I have only completed problems by taking the natural log...

suppose f is a continues function on point x_0 prove that g(x)=(x-x_0)*f(x) differentiable on x_0?? calculate g'(x_0) i tried to think like this: if f(x) is continues on x_0 then lim f(x) as x->x_0 equals f(x_0) mvt says f'(c)=[f(a)-f(b)] cauchys mvt says...

Homework Statement What is the integral of: y + x \frac{dy}{dx} The Attempt at a Solution I know that it is xy, after implicit differentiation. However, I cannot get it without prior knowledge of implicit differentiation.

Homework Statement Find the derivative of the following function f. Homework Equations f(x)=x^log(x) The Attempt at a Solution I really don't know how to do this, as it's x to the power of a function of x.

Homework Statement Given two quantum preparations \frac{1}{\sqrt{2}} \left( |0\rangle + | 1 \rangle \right) \frac{1}{\sqrt{2}} \left( |0\rangle - | 1 \rangle \right) Give a measurement that will distinguish between these two preparations with high probability. The Attempt at a...

Hey I'm stuck on a problem, i have to find the differential of y=5x(2x-1)^3 and therefore find the x-coordinate of a stationary point on a graph, I use the chain rule and get the differential to be 30x(2x-1)^2 and therefore the x-coordinate to be 0.5 however my textbook says the differential...

Hey guys I am having a bit of trouble solving the following problem, differentiate y = x ((1+x)^0.5) I am using the product rule however I am getting a different answer to the back of my textbook I was wondering if anyone could help clear this up for me, thanks.

Let f be continuous on [0,1] and differentiable on (0,1) such that f(0)=f(1), prove that there exist a 0 < c < 1 such that f\acute{}(1-c) = -f\acute{}(c). thanks for any suggestions.

Homework Statement Let y = tan2(3x-2) Find dy/dx The solution is: 2*tan(3x-2)*sec(3x-2)*3 = 6*tan(3x-2)*sec2(3x-2) Why is it not: 6*tan(3x-2)*sec(3x-2) I am thinking: y = (tan(3x-2))2 take the power 2 down,multiply with the parentes multiply with the defferentiated parentes...

I'm trying to understand how Randall and Sundrum go from Eq. (9) to Eq. (10) in their RS1 paper: http://arxiv.org/abs/hep-ph/9905221 I understand that since the extra dimension \phi is periodic, we must have \frac{d^2}{d\phi^2}|\phi|\propto \delta(0) - \delta(\phi - \pi). However...

Homework Statement If y^2 - 2xy=21, then dy/dx at the point (2,-3) is ? Homework Equations y^2 - 2xy=21 The Attempt at a Solution I know that I have to differentiate the function. I just do not know how to do it: implicitly or explicitly.

Homework Statement Define f(0,0)=0 and f(x,y)=\frac{x^{3}}{x^{2}+y^{2}} if (x,y)!=(0,0) Let \gamma be a differentiable mapping of R1 into R2, with \gamma(0)=(0,0)\;and\; |\gamma'(0)>0|. Put g(t)=f(\gamma(t)) and prove that g is differentiable for every t in R1 Homework Equations...

Homework Statement suppose f is a differentiable mapping of R1 into R3 such that |f(t)|=1 for every t. Prove that f'(t)\cdot f(t)=0. I guess it is more proper to write (\nabla f)(t) \cdot f(t)=0, where (\nabla f)(t) is the gradient of f ant t. Homework Equations The Attempt at a...

So we are given T(t) = c'(t)/||c'(t)|| as well as ||T|| = 1 We also know T(t)dotT(t) = 1 and T'(t)dotT(t) = 0 The problem asks us to find T'(t) I tried differentiating c'(t)/||c'(t)|| treating ||c'(t)|| as the square root of the dot product of c'(t) with itself. I used the product...

Homework Statement Suppose A is a real nxn matrix and f: R^n --> R is definted by f(v)=v^tAv (where v^t denotes the transpose of v). Prove that the derivative of f satisfies (f'(v))(w) = v^t (A+A^t)w Homework Equations The Attempt at a Solution I'm kinda lost here and I really...

Homework Statement The problem reduces the derivative (dZ/d(1/V)) to (dZ/dV) x (dV/d(1/V)), where Z is the compression factor and v is molar volume. It further shows that it equals -V^2(dZ/dV). I don't know how they arrived at that value because by my logic it should be 1/(-V^2)...

hi, I want to know the practical use of Integration and Differentiation. I know what it is. I just want to know how can i explain it with a practical example. example : for Differentiation - the dy/dx can be explained that y is dependent on independent variable x. How can d2y/dx2 be...

Homework Statement find d^2y/dx^2 at (1,1) for: x^2y + x^2 -y^2 = 1 Homework Equations none The Attempt at a Solution i worked it all out but the answer I am getting is not an option. could someone show me where i made a mistake? I am not asking you to do the problem for me...

Hi, I'm confused about what differentiation on smooth manifolds means. I know that a vector field v on a manifold M is a function from C^{\infty}(M) to C^{\infty}(M) which is linear over R and satisfies the Leibniz law. This should be thought of, I'm told, as a 'derivation' on smooth...

Homework Statement Let f be continuous and differentiable on [a,b], and suppose that f attains its maximum and minimum points c and d, respectively, where c,d belong to [a,b]. Show that f ' (d) = 0 Homework Equations The Attempt at a Solution I thought about using the Mean...

I am having trouble remembering the correct approach here. This is in regards to deriving a governing equation for conservation of momentum for a non-Newtonian fluid. I thought about posting in engineering, but it is more of a calculus question: d/dx(((-dv/dx)^(m-1))*(dv/dx)) where we are...

I was looking at results of different numbers in the equation \sqrt[x]{x} and found out that the biggest result came when it was \sqrt[e]{e}. I know this can be re-written as x^{1/x} and that the gradient would be 0 at x = e. How would you differentiate y = x^{1/x}, I can't seem to do it using...

Can I differentiate a complex function, like e^{-if(t)}?

Homework Statement For the function of two variables f(x,y)=tan^-1(y/x) find df/dx and df/dy I know i just differentiate with respect to x and then to y but I'm stuck on the tan^-1(y/x) I know tan^-1(x)=1/1+X^2 when I applied this with respect to x I get 1/-1+y I think this is wrong...

I saw the argument for complex differentiation today and I had a question about a 'well known' aspect of the argument. My professor said something like this (at least a version of it): Derivatives on complex variables are defined in the usual way. However, in the complex plane, delta(z) may...

Homework Statement Show using cartesian components that d/dt(a.b)=(da/dt).b+a.(da/dt) The Attempt at a Solution a= axi+ayj+azk b=bxi+byj+bzk a.b=axbx+ayby+azbz d/dt(a.b)= d/dt(axbx+ayby+azbz)

Homework Statement A man 6 feet tall walks at a rate of 5 feet per second toward a streetlight that is 30 ft high. The man's 3 ft tall child follows at the same speed, but 10 feet behind the man. At times, the shadow behind the child is caused by the man, and at other times, by the child...

Homework Statement Let Δf= d^2f/dx^2+ d^g/dy^2 (laplace equation - Partial Derivatives) Show Δ(f(g(z))= Mod(g'(z))^2 * Δf(w,v) where g(z)=w(x,y)+v(x,y)i Homework Equations we propably need to use cauchy riemman equations: dw/dx = dv/dy and dw/dy = - dv/dx and chain rule The Attempt...

Homework Statement what is the implicit differentiation ? Homework Equations 2sin(x)cos(y)=1 The Attempt at a Solution d/dx[2sin(x)cos(y)]= d/dx[1] 2cos(x)*-sin(y)*dy/dx=0 I haev a bad feeling i did this wrong...

hi i couldn't solve this question i think there is a mistake in it anyone can check it please ? http://img296.imageshack.us/img296/3716/13055173zr3.png

Hi all, I have to differentiate Ln(x+\frac{1}{x}) where I first differentiate Ln and than multiply by the differentiation of the inner function 1/(x+\frac{1}{x})*(1-\frac{1}{x^2} which I simplify to \frac{x}{x^2+1}*(1-\frac{1}{x^2}) \frac{x}{x^2+1}-\frac{1}{x*(x^2+1)}...

Homework Statement f(x)= x^2(x-2)^4 solve for f '(x) Homework Equations f(x) = x^2(x-2)^4 The Attempt at a Solution 4x^2(x-2)^3 The answer is given in the book as 2x(x-2)^3(3x-2) i'm not following any progression that gets me to that solution regardless of how many times I...

Homework Statement f a differentiable real valued function lim h - > 0 of (f(x + ah) - f(x + bh))/h where a,b real numbers Homework Equations definition of derivative lim h-> 0 of (f(x+h) - f(x))/h The Attempt at a Solution I've picked several functions like x^2 and 1/2x...

Homework Statement I need in proving that the derivative (d^{n}/dx^{n})(sin4x + cos4x) = 4n-1 cos(4x + n\pi/2) The Attempt at a Solution I understand implicit differentiation in basic problems but I get stump with the n exponent in the differentiation symbol; am I suppose to treat it as...

Homework Statement I am given a table of data derived from experiment. A force (F) is applied to a spring and the extension (x) is measured and recorded. An additional column of data for the derivative (dF/dx) is also provided. Here is the data: x(m) F(kN) df/dx (kN/m) 0.0...

Homework Statement Find the coordinates of the point in the first quadrant at which the tangent line to the curve x3-xy+y3=0 is parallel to the x-axis. SO: x= + y= + mtan=0 Homework Equations \frac{dy}{dx}=m_{tan} The Attempt at a Solution \frac{dy}{dx}=\frac{y-3x^{2}}{3y^{2}-x}=0 After I...

I encountered a proof problem when I was reading up on the derivatives of natural logarithms' section. It gave a rule which said this : \text{For } a >0 \text{ and } a\ne 1 \text{,}\\\frac{d}{dx}(a^{u}) \ = \ a^{u} \ \ln{a\frac{du}{dx}} To prove it on my own, I made a few identities: a^{u}=y...

Suppose we are given that d --F(y) = f(y) dy Then is it true that dF(h(u)) -------- = f(h(u))[/color] dh(u)/du ? du Why or why not? In particular, I don't understand how to get the red part... Thanks for explaining!

What is the actual meaning of the notation of df[g(x)] ------- dx Here do we actually differentiate f with respect to x first and then evaluate it at g(x), or do we first evaluate f at g(x), then differentiate it with respect to x? Does the order matter? df --[g(x)] dx d...

1) A particle is moving along the curve y=3sqrt{3x+3}. As the particle passes through the point (2, 9), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant. 2) Use implicit differentiation to find...

Homework Statement Hello guys. I had to do some test corrections for my AP Calculus AB class. I have completed all of them besides the four below. Can anyone tell me where I go wrong? 1. Differentiate y = (1+cosx)/(1-cosx) dy/dx = [(1-cosx)(sinx)-(1+cosx)(sinx)]/(1-cosx)^2...

Homework Statement Use implicit differentiation to find the slope of the tangent line to the curve 4x^2-3xy+1y^3=26 at the point (3,2) The Attempt at a Solution I attempted the problem and i came up with dy/dx= (-8x+4)/(3y^2) which is wrong. Need some help with this.

Homework Statement Determine dy/dx when y*sin(x2)=5 The Attempt at a Solution y*2xcos(x2) dx/dx + sin(x2)*1 dy/dx = 0 2xy cos(x2)*dy/dx = -sin(x2) dy/dx = -sin(x2) / 2xy cos(x2) dy/dx = -2xy tan(x2)

Homework Statement Find the value of dy/dx at x=2 when x2+xy=5 The Attempt at a Solution To find y: 22+2y=5 y=1/2 To find dy/dx: 2x(dx/dx)+x(dy/dx)+y(dx/dx)=0 2x+x(dy/dx)+y=0 (dy/dx)=(-2x-y) / x Plug in y and x: dy/dx=-2(2)-(1/2) / 2 dy/dx=-9/4 when x=2

Homework Statement Find dy/dx for: a) xsin(xy^2) - ln(x/y) = y b) x = 3cos(a), y = 2sec(a). simplify then find dy/dx when a = pi/3 Homework Equations The Attempt at a Solution I've done both of them, was just hoping someone could check I've done things correctly. I'm...

Homework Statement Find the partial of z with respect to x keeping r constant. Homework Equations z=x2+y2 x= rcos(t) y= rsin(t) The Attempt at a Solution= r^2(cos(t))^2 + r^2(sin(t))^2 use product rule on "x" and hold r and y constant = [0(cos(t))^2 + r^2(2cos(t))(-sin(t)))] + 0...

Homework Equations Take the second derivative of: cos(x^2) The Attempt at a Solution cos(x^2) dy/du = -sin(u) du/dx = 2x dy/dx= -2xsin(x^2) I don't know how to begin taking the derivative of this a second time...