Question

I need help question

Answer 1

The given function f is given by:

`f(x)=(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,

`(du)/(dx)=5x^4-7`

and

`f(x)=(1)/(u^8)`

Therefore,

`f^(\prime)(x)=(df)/(du)*(du)/(dx)`

Since f = 1/u⁸, it follows that:

`(df)/(du)=-(8)/(u^9)`

Therefore,

`\begin{gathered} f^(\prime)(x)=-(8)/(u^9)*(5x^4-7) \\ =-(8)/((x^5-7x+6)^9)*(5x^4-7) \end{gathered}`

Therefore,

`f^(\prime)(x)=(8(7-5x^4))/((x^5-7x+6)^9)`

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