Question

Use the differentiation rules developed in this section to find

the derivatives of the functions

$f\left(x\right)=4-x^7$

Short answer

The derivative of$\mathrm{f}\left(\mathrm{x}\right)=4-{\mathrm{x}}^7\mathrm{is}-7{\mathrm{x}}^6$

Step-by-step solution

Step1. Given information

Here function $f\left(x\right)=4-x^7$is given.

we have to find out the derivatives of this function

Step2. finding the derivatives of the function

By using the power rule, we can solve this problem.

Power rule: For any nonzero rational number k,

$\frac{d}{dx}\left(x^k\right)=k{x}^{k-1}$

Thus using this power rule when we do the differentiation , we get

$$\begin{gathered} \frac{d}{d\mathrm{x}}(4-{\mathrm{x}}^7)=\frac{d\left(4\right)}{d\mathrm{x}}-\frac{d\left({\mathrm{x}}^7\right)}{d\mathrm{x}} \\ =0-7{\mathrm{x}}^6\mathrm{since}\mathrm{derivative}\mathrm{of}\mathrm{a}\mathrm{constant}\mathrm{is}0 \\ =-7{\mathrm{x}}^6 \\ \mathrm{thus}\mathrm{the}\mathrm{derivative}\mathrm{of}\mathrm{given}\mathrm{function}\mathrm{is}-7{\mathrm{x}}^6 \end{gathered}$$