Find the value of (f ◦ g)' at the given value of x.
f(u)=1/(cos^4 u) -1 , u=g(x)=pi x , x=10

I got -1 as an answer but its not an answer choice

Question

Find the value of (f ◦ g)' at the given value of x.
f(u)=1/(cos^4 u) -1 , u=g(x)=pi x , x=10

I got -1 as an answer but its not an answer choice

anonymous · Answer

Ok. So (f o g)' is taking derivative of function over function.

$$f(u) = \frac{1}{\cos^4 u} -1 ; u = g(x) = \pi x$$
$$f \prime = -4 \cos^{-5} u (-sinu) u \prime = \frac{4sinu}{\cos^5u} \pi$$
Substitute u = 10pi then we obtain
$$f \prime = \frac{4\pi \sin10\pi}{\cos^5 {10\pi}}$$
But $$\sin (10\pi) = \sin (0 + 5.2\pi) = \sin (0) = 0$$
Then the answer is 0

anonymous · Answer

thats not an answer choice. they are:
-pi
-10pi
10pi
4-pi

anonymous · Answer

Could you please use equation editor to type f(u) again. I am confused between 
$$f(u) = \frac{1}{\cos^4 u} - 1$$ or
$$f(u) = \frac{1}{\cos^4 u - 1}$$

anonymous · Answer

the first one you wrote down. im on mobile so its hard to do the equation writer.

anonymous · Answer

I cannot find another solution, please check your question again. Actually, the method is taking the derivative of function f over function g. Then I did it, with sin 10pi = 0, we have the answer should be 0