Question

I need help question

Answer 1

The given function f is given by:

$f(x)=\frac{1}{(x^5-7x+6)^8}$$\begin{gathered} \text{ Let }u\text{ be a function given by:} \\ u(x)=x^5-7x+6 \end{gathered}$

Therefore,

$\frac{du}{dx}=5x^4-7$

and

$f(x)=\frac{1}{u^8}$

Therefore,

$f^{\prime}(x)=\frac{df}{du}\times\frac{du}{dx}$

Since f = 1/u⁸, it follows that:

$\frac{df}{du}=-\frac{8}{u^9}$

Therefore,

$\begin{gathered} f^{\prime}(x)=-\frac{8}{u^9}\times(5x^4-7) \\ =-\frac{8}{(x^5-7x+6)^9}\times(5x^4-7) \end{gathered}$

Therefore,

$f^{\prime}(x)=\frac{8(7-5x^4)}{(x^5-7x+6)^9}$

.