How do I find the solution to this derivative problem?

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Homework Statement


Two functions f and g are such that f(4)=3, f prime (4)= -2, g(4)=7, and g prime (4)=5. Determine (1/g^2) prime(4). By "prime" I mean when there is something that looks like a little "1" exponent on the letter.

Please help and give clear step by step explanations. Thanks.


Homework Equations


N/A


The Attempt at a Solution


I know what is the quotient and product rules are, but I have no idea how to approach this question.
 
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Have you learned the chain rule yet?

My hint is: what is the derivative of
\frac{1}{[g(x)]^2}?
 
n!kofeyn said:
Have you learned the chain rule yet?

My hint is: what is the derivative of
\frac{1}{[g(x)]^2}?

Is it -2g(x)^-3 x g(x)?
 
Hint #2:
Chain rule: f(g(x)) = f'(g(x))g'(x)

In this case...
f(g(x)) = g(x)^-2

Soooo...
 
Cuisine123 said:
Is it -2g(x)^-3 x g(x)?

Exactly. Now evaluate your expression at x=4.

Also, don't use x for multiplication. * would work better. :)
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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