# Thread: Derivative of Composition of Functions Question

1. ## Derivative of Composition of Functions Question

Heylo <3

I have the answer to the question, but I can't seem to quite get to it successfully.

Let f(x)= x^5 and g(x)= 2x-3, Find (g o f)(x) and (g o f)'x

-Finding (g o f)(x) -->
f(x) = x^5
g(x^5)= 2x^5-3
Which is the correct answer for part 1

-Finding (g o f)'(x) -->
g'(f(x))(f'(x))
g'(x^5)(5x^4)
10x^4 * 5x^4
= 50x^8

2. Originally Posted by StarlitxSunshine
Heylo <3

I have the answer to the question, but I can't seem to quite get to it successfully.

Let f(x)= x^5 and g(x)= 2x-3, Find (g o f)(x) and (g o f)'x

-Finding (g o f)(x) -->
f(x) = x^5
g(x^5)= 2x^5-3
Which is the correct answer for part 1

-Finding (g o f)'(x) -->
g'(f(x))(f'(x))
g'(x^5)(5x^4)
10x^4 * 5x^4
= 50x^8
The best approach is to just write out the composite function and differentiate. If $\displaystyle f(x)=x^5$ and $\displaystyle g(x)=2x-3$, then $\displaystyle g(f(x))=2(x^5)-3$.
If you differentiate this, you should get $\displaystyle 10x^4$.