Q. 8 - Calculus

Question

Explain why the power rule cannot be used to differentiate the function ${(2-x)}^{\frac{1}{3}}$

Step-by-Step Solution

Answer

As we have not calculated the derivative of the term (2-x) power rule cannot be used here.

Step 1: Given information

We are given a function ${(2-x)}^{\frac{1}{3}}$

Step 2: Explaination

By using the power rule We get the differentiation as

$$\begin{gathered} \frac{d}{dx}\left({(2-x)}^{\frac{1}{3}}\right) \\ =\frac{1}{3}·\frac{1}{{(2-x)}^{{\displaystyle \frac{2}{3}}}} \end{gathered}$$

But in it we have not calculate the derivative of term (2-x) which is -1

Hence power rule cannot be used to find the derivative of the function