Differentiate Definition and 223 Threads

Homework Statement Differentiate x^{x^2}, with respect to x Homework Equations \frac{d}{dx} (x^{x^2}) The Attempt at a Solution I arrived at... (ready?) (ta dah!): x^{x^2}.(2x.\ln(x)+x) I'm pretty confident this is wrong... I went y(x)=x^{x^2}, then took the natural...

i have a final coming up on wednesday and my professor will post 8 different differential equations without telling us which method to use. i want to know (generally speaking of course) which method would work for certain types of second order differential equations. for instance, judicious...

hiya, do you mind checking my awnsers please? i think i may have gotten them all wrong. a: y= sin(3x)/x^2 b: (x^3) * (cos(4x)) c: If dy/dx =5/x and y=6 when x=0, then y= d: if ln(x^3) - ln(x) = 4, then x=e^something e: if dy/dx = 3e^x, and y = 7 when x =0, then y = my...

1: Sin(4x^2) * 8x 2: Ln(3x) / x^2 3: If dy/dx = 2ex and y=6 when x=0, then y = 4: If ln(x^3) - ln(x) = 12, then x=e^(blank) 5: evaluate the integral by integrating it in terms of an area (not sure how to use latex) integral from 1/2 -> 3/2 (2x-1)dx my attempts =] 1...

1: U=e^(-2t) 2: Y=e^(4(x^3)-3x) 3: T= x^2/3 * e^-3x q4: find the equation of the curve passing through the point (1,2) and having the slope at the point (x,y) given by dy/dx = 3/x q5: find dy/dx when y^2 + (y^3)*(e^y) = xy + ln(3x) q6: Find f If F'(x) = 5e^x and f(0) =...

Homework Statement hey guys, got a question. how do you differentiate y=ln(1+x^2)^1/2. any help would be appreciated, thanks Homework Equations answer is x/(1+x^2) The Attempt at a Solution

Homework Statement differentiate (x2)lnx im having a blonde moment...how do you start?

Homework Statement Differentiate... (3x+4)^7 (7x-1)^3 and simplifyHomework Equations Chain rule and Product rule The Attempt at a Solution I got (splitting the components up to substitute into the product rule) and using the chain rule \begin{align*} \\f(x) = (3x+4)^7\\ f'(x) =...

Homework Statement Hi all. I have a time-dependent variable called x. I wish to differentiate x2 with respect to the time t, and this is what I have done: \frac{d}{dt}x^2 = \frac{d}{dx}x^2\frac{dx}{dt} = \frac{d}{dx}x^2\dot x. where the dot over x denotes differentiation with...

I just need a short reminder from Calculus. Suppose you have a linear functional \alpha from C1[-1,1] to \Re, given by \alpha(f) = \int_{-1}^{1}f(t)g(t)dt for some fixed continuous function g. What is \frac{d \alpha}{d f}?

How do you differentiate f(x)=arctan(e^5x)

I don't really know how to even start this problem because I don't think the product rule would work here since there are three variables, right? Here is my attempt at it: xe^x csc x xe^x csc x + xe^x (-csc x cot x) xe^x (csc x - csc x cot x) Used the product rule and that's what...

Homework Statement Can some body differentiate laplace,fourier,Z-transforms? Homework Equations The Attempt at a Solution they are related to engineering field. Z-transforms used in discrete signals?

how many times can we differentiate this function?? how many times can we differentiate this splitted function on point x=0 ?? f(x) = \{ x^{2n} \sin (\frac{1}{x}) ,x \ne 0 \{ 0,x = 0}} \\

Homework Statement The problem is to differentiate the function. y=cos4(x2 + ex) Homework Equations cos(x)'= -sin(x), (xn)'=n*xn-1, (ex)'=ex*x' The Attempt at a Solution Thought it would be the chain rule. Here's what I came up with: y'=4cos3(-sin(x2 + ex)(2x + ex) Is this...

i need to differentiate the following: sqrt[10/(4+x)] so i re-wrote it as: [10(4+x)^-1]^1/2 but am getting very confused when i try to differentiate it. any help would be great! cheers

Homework Statement Compare the following situations (a) and (b): (a) A beam of atoms, half of which are preselected as “+ in z”, the other half as “− in z”, is sent through a Stern-Gerlach apparatus that ...(A) sorts in the z direction...

Homework Statement I'm supposed to differentiate a function: (x^3) + 2x Using the standard way used today, and then find the equation of the line so that it passes through (1,3). So I did: 3(x^2) + 2 and then the final equation is y = 5x - 2 right? Then I'm also supposed to differentiate and...

Homework Statement a)How to differentiate fx=e^|x|? b)Why when x = 0, f'(x) is undefined Homework Equations The Attempt at a Solution Is it d/dx e^|x| = e^|x|? I have no idea for this question.

Homework Statement Differentiate y=\ln(e^{-x} + xe^{-x}) Homework Equations - Logarithmic differentiation? The Attempt at a Solution Here goes: y=\ln(e^{-x} + xe^{-x}) y'=\frac{e^{-x} + (x\frac{d}{dx}e^{-x}+e^{-x}\frac{d}{dx}x)}{e^{-x}+xe^{-x}})...

Homework Statement Differentiate the function f(u)=\frac{\ln u}{1+\ln(2u)} Homework Equations - Quotient rule? - Logarithmic differentiation? The Attempt at a Solution I just learned about logarithmic differentiation so I think the idea here was to use logarithmic...

Differentiate the function g(u) = √2u + √3u y = (x^2 - 2√x)/(x) y = (e^x)/(1 + x)

Homework Statement Find the minimum value of |log_{b}a+log_{a}b| where 'a' and 'b' are positive numbers. First tell me, do I need to differentiate it? If no, then how can this thing be done? I don't know how to differentiate a equation with three variables and that too with modulus...

Is there special name for numbers that are to the power of themselves e.g. X^X; 3^3; 4^4 And how can you Differentiate X^X...Thanks

i can differentiate most other simple functions.. .though can someone please help me to understand why the derivative of f(x)=-5/3x is simply 5/3x^2?

Homework Statement Given that y = lnsecx, - pi/2 <=x<=0, use the substituation u = secx, or otherwise, to show that dy/dx = tan x. The Attempt at a Solution well i thought about using the product rule, but you as it's ln(secx) not lnxsecx (2 different functions)... soooo I am all out of...

Homework Statement Part of a question here... Show that \frac{d}{dx} \left[ \frac{x}{(4-x^2)^n} \right ] = \frac{1-2n}{(4-x^2)^n} - \frac{8n}{(4-x^2)^{n+1}} Homework Equations \frac{d}{dx}(\frac{u}{v}) = \frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2} The Attempt at a Solution...

How do I differentiate f(x,t) = expi(kx-wt) f'(x,t) = ? f''(x,t) = ?

Homework Statement RE: F(y)= (1/y\hat{}2 - 3/y\hat{}4)(y+5y) the answer is: F=5+14/y\hat{}2+9/y\check{}4 The Attempt at a Solution F(y)= (f*g)\acute{} f\acute{}*g)+(f*g\acute{}) (-2y\hat{}-3+12y\hat{}-5)*(y+5y\hat{}3)+(y\hat{}-3-3y\hat{}-4)*(1+15y\hat{}2) so, I get...

1. Homework Statement [/b] F(y)= (1/y^{}2 - 3/y^{}4)(y+5y^{}3) Homework Equations the answer is: F\acute{}(y)=5+14/y^{}2+9/y^{}4 The Attempt at a Solution In order to use the product formula I brougth the first parenthesis to a common denominator y^{}4 and then tried to use the...

Homework Statement if f(x,y) is e^(x+y) am i right in saying dy/dx is e^(x+y) Homework Equations The Attempt at a Solution

It is a simple math question, but I am stuck. The law of cosines is R^2=h^2 + r^2 - 2 h r cos (theta). Theta is of course the angle facing R. To differentiate, I first set r^2 - 2hr cos\Theta+ (h^2-R^2) = 0 2 r \dot{}r - 2 h cos\Theta \dot{}r + (h^2-R^2) = 0. Is there any...

Homework Statement need to differentiate: f(x) = ln(x^4sinx^2) Homework Equations The Attempt at a Solution just use ln 1/x and differentiate the sins and exponents to get what's below. would this be the final form? f'(x) = 4*(1/x) + 2*(cosx/(sinx)

I'm practicing how to differentiate equations. I need help differentiation this: http://img127.imageshack.us/img127/531/voloz4.jpg I made that equation up from a soda cup, different size bases. Is this equation correct? I tried to differentiate with respect to time. I get...

Homework Statement ln ln ln x^3 Homework Equations The Attempt at a Solution My teacher was going over the review for the final and this was one of the questions. He said the answer is 1/ln ln x^3 but I don't know how to get that...can someone please help me...thank you!

please explain in more detail on how we come up with the answers below. Thanks in advance! (formulas much appreciated) Differentiate: 1 y=e^x =e^x 2 y=lnx =1/x

Homework Statement How do u implicitly differentiate (xy)^1/2 Homework Equations The Attempt at a Solution Would it be 1/2(xy)^-1/2 multiplied by 1 and dy/dx. Thanks

Hi everyone, I'm new to this forum... I hope I've posted in the right section... How do I differentiate y=2e(2x+1) using the chain rule? I let u= (2x+1) so du/dx = 2 but how do I differentiate y= 2eU ? thank you :)

Homework Statement differentiate the given function: y=2/x^2 -1/x^3 +1/2^3 Homework Equations The Attempt at a Solution 2(-2x^3) -1(-3x^4) -4x^3 + 3x^4 my book says the answer is: how do you go from my notation to the one my book uses?

Hello, I have an integral F(x) = \int\limits_a^x f(x) d(g(x)) and g(x) may and may not be differentiable. How can I differentiate d(F(x)) ? Thanks

this is an even problem of my homework so there is no answer i think i did it right, i would just like a thumbs up/down ... thanks y=2^{3^{x^{2}}}} \ln{y}=\ln2^{3^{x^{2}}}} \ln{y}=3^{x^{2}}}\times\ln2 \frac{y'}{2^{3^{x^{2}}}}}=\ln2\times3^{x^{2}}}\times\ln3\times2x...

for my Schrodinger equation I need the second derivative of this: Axe^(-x^2/ L^2) I think that I am missing some chain rule or something. The solutions say: ( 4Ax^3-6AxL^2)(1/L^4)e^(-x^2/ L^2) I only got -2Axe^(-x^2/L^2) for the 1st deriv. and 4Axe^(-x^2/L^2) and I still can't...

Hi all, I have a qustion. dB/ds= -TN, dU/ds= KN (1) N= U x B (2) dN/ds=TB-KU (3) How Eq.(3) can be obtained from Eq.(1),(2)? Have a nice day!

How do you differentiate the likes of (sinx)^2 thanks

Hi, I am stuck in a differentiation problem. I need to find the derivative of an integration of an unknown function with respect to the function itself, and then set the derivative to zero in order to find the form of the funtion which gives the minimum of its integration. For example, find a...

Hey Guys, this is one of the Q's in my book which I have completed but would just like to check whether (a) it is correct and B whether I can leave it in this format for the answer? cheers I used the fundamental theorem part 1 and the chain rule due to upper limit of integration being x^3...

Homework Statement Differentiate the following with respect to x leaving in the simplest form \frac{d}{{dx}}\left[ {\ln \left[ {\left( {1 - \sqrt x } \right)^2 \left( {1 + \sqrt x } \right)^3 } \right]} \right] Homework Equations The chain rule \frac{d}{{dx}}\left[ {\left( {f\left(...

x^2y the y is biglike the x its not small and how do you differentiate this xy^2 for the first one i used the product rule and thesecond one and i get a different answer then what i was suppost to get

y=x^2+4x+3/square root x i did this s x^2+4x+3) square root x/ sq x * sq x sq x *x^2)+4x*sq x+ 3/1

y=ex(x is suppost to be smaller and on the top right of e)/x squared i a suppost to differentiate this, well i wrote -2ex/x cubed+ ex/ x sq. now u probabl might be confused by the way i wrote it since i don't know how to put the right things for my problems, well i set up the problem...