Q. 7 - Calculus

Question

Explain why the power rule does not say that the derivative of $3^x$ is $x{3}^{x-1}$. Especially why doesn't $3^x$ fit the pattern for the power rule to apply

Step-by-Step Solution

Answer

As the function is of the form constant raised to a variable its differentiation is not $x{3}^{x-1}$.

Step 1: Given information

We are given a function $3^x$

Step 2: Explaination

First of all the function is not of the form $x^3$ but it is $3^x$ and also the derivative of $3^x is 3^x{\log }_e\left(3\right)$