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Q.35

Expert-verified
Found in: Page 198

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# Use the differentiation rules developed in this section to findthe derivatives of the functions$f\left(x\right)=4-{x}^{7}$

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

See the 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

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