f(t) = 8(t^4 − 6)^5

find f'(t)

How is this incorrect:

8(5)(t^4-6)^4 - general power law?

SOLVED:

40\left(t^4-6\right)^4\left(4t^{\left(3\right)}\right)

f(x)=((x+8)/(x-8))^5

f'(x)=5((x+8)/x-8))^4

how is this wrong?


edit: figured out about the quotient rule but somehow this is still wrong

5\left(\frac{x+8}{x-8}\right)^4\left(\frac{\left(x-8\right)-\left(x+8\right)}{\left(x+8\right)^2}\right)

wtf?

Edited 10/2/2019 02:50:25

I'm pretty sure you were supposed to take as

(x + 8)^5
__________
(x - 8)^5

you have a variable in both sides of the division bar

https://www.wolframalpha.com/input/?i=d%2Fdx%28%28x%2B8%29%2F%28x-8%29%29%5E5

Thanks dude, but I already submitted the online homework.

Whenever you have a function f(g(x)), you take the derivative of f(g(x)) while considering g(x) as a constant and multiply that by the derivative of g(x). So d/dx[f(g(x))] = f'(g(x)) · g'(x)