Q.35 - Calculus

Question

Use the differentiation rules developed in this section to find

the derivatives of the functions

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

Step-by-Step Solution

Answer

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

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 

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