# differentiating

2. ### Differentiating fractions without the quotient rule?

Differentiate y=\frac{x^{2}}{(x+4)} without using the quotient rule. Can you use the product rule to differentiate above? If so, what are the steps? y=x^{2}(x+4)^{-1} \frac{dy}{dx} = 2x(x+4)^{-1}+x^{2}(1)^{-1} Is the above correct so far? If not, where did I make the mistake? :)
3. ### Help with differentiating a tricky function

Hello everyone, I am a new user and this is my first post. As a bit of background ... I haven't done much serious maths for about 40 years now. In the early 1970's I studied Astronomy and Physics at Glasgow University and so also had to study university-level Mathematics which was compulsory for...
4. ### Differentiating the integral by parameter

Hi, sorry for the stupid question, but how to find the following derivative?
5. ### Differentiating Inverse Trig Functions

Hi, I'm stuck with Q1. (e) on the attached file. I can do (a) - (d), it's just the x^2 at the front that's throwing me off. I've tried just differentiating the sin^-1(x/2) on it's own as done previously but that doesn't seem to help. Help would be greatly appreciated, thanks!
6. ### Differentiating a piece-wise function

I'm supposed to be differentiating f(x) = {x2sin(1/x) if x ≠ 0, 0 if x = 0}, once at f(x) = 0 using f'(x) = limf(x+h) - f(x)/h, and also by finding the lim f'(x) as x → 0 using product and trigonometric laws for derivatives. In the first case, I get f'(0) = 0, and in the second I get that the...
7. ### Differentiating an absolute function

Could someone please explain how to differentiate absolute functions? This is what I'm stuck on at the moment. f(x)=5-|x-5| I'm not aware of any rules for differentiating it, but they seem to pop up in my practice problems quite often. Any help is appreciated!
8. ### Differentiating sin(x/y)

How do we differentiate something like this? Chain rule should be used here, so the first term will be cos(x/y), but then I don't understand how to break up this (x/y) function?
9. ### Differentiating natural log function

$f(x)=a^x=(a)^x=(e^{\ln a})^x=e^{x \ln a}$ $f'(x)=$? I don't quite understand how the Chain Rule is applied here and what is the inner\outer function? Could someone elaborate? PS Oops, I meant natural exponential function.
10. ### Need help differentiating

i= v/r (1-e^-Rt/L) How would i go about differentiating this formula to get di/dt? Would I use the product rule or another rule?
11. ### Differentiating: The product rule

How would you go about differentiating this? g(x)=(x^3) (e^x) I tried using the product rule and this is what I have: g'(x) = (3x^2)(e^x) + (xe^x^-^1 )(x^3) but I saw online that the answer is g'(x) = (3x^2)(e^x) + (e^x )(x^3) What did I do wrong? Edit: I have only touched on the basics of...
12. ### differentiating maclaurin series

I have to differentiate the MacLaurin series for xe^x and use the result to show that \sum_{k=0}^{\infty} \frac{k+1}{k!} =2e x*\sum_{k=0}^{\infty} \frac{x^k}{k!} = x[1+x+\frac{x^2}{2!}+\frac{x^3}{3!}....] = x+x^2+\frac{x^3}{2!}+\frac{x^4}{3!}.... = \sum_{k=0}^{\infty} \frac{x^{k+1}}{k!} From...

There are 96 persons at a retreat. If, at t=0, 8 are infected, and after 4 days this has doubled, how many will have the disease 8 days after t=0? Assume rate at which it spreads is proportional to the number of contacts and that both groups move freely, so the number of contacts is proportional...
14. ### Differentiating an Integral

I haven't been able to figure out exactly how the author of this statistics book got the following. From, E[C_t(X)]=ct\int_0^tf(x)dx -c\int_0^txf(x)dx+k\int_t^\infty xf(x)dx-kt\int_t^{\infty}f(x)dx to, \frac{d}{dt}E[C_t(X)]=ctf(t)+cF(t)-ctf(t)-ktf(t)+ktf(t)-k[1-F(t)] I think I have to fully...
15. ### Differentiating Implicit Equations

If sin^4(\[Alpha])/x+cos^4(\[Alpha])/y-1/(x+y)==0 ^^^^(it looked fine in mathematica...can someone tell me how to write code in this forum?) then what is dy/dy??*here [alpha] is a constant* well i figured out dy/dx and it came out to be y/x but the book says dy/dx=tan^2[Alpha],which is a...
16. ### Differentiating an integral-defined function

hi, i have a problem with differentiating please help (I think) It is well known that for an integral-defined function, differentiating them with the upper limit(i.e. 'x') takes the integral away. (*) i.e. \frac{d}{dx}\int_{0}^{x}\ f(t) \ dt = f(x) The problem is, I came across a weird...
17. ### differentiating a complex function

Hi, any help to prove that?
18. ### Forming an equation and differentiating it

So you need to find an optimum price, so I just thought you had to find a stationary point, i.e. when the differentiation equals 0 But if you differentiate Q you just get -80. So you can't set this to 0, nor can the optimum price be -80. So I thought, ok it must be a bit harder than that. So...
19. ### Differentiating sin(2x)^2

I'm trying to differentiate \sin^2(2x) but it's not going very well. The answer is 2sin(4x). To me it seems natural to use the chain rule and get 2sin(2x) and then multiplied with the derivative of sin(2x) which is 2cos(2x). So my gut tells me the answer is 2sin(2x)*2cos(2x) but that's...
20. ### Differentiating y

I can't seem to wrap my head around differentiating y or f(x). For example: x^2+xy^2=2. I understand the product rule and everyone keeps saying that ''it's just the product rule'' when I'm differentiating implicitly like that, but I don't have the intuition, it's just missing. Can someone...