Q 26. - Calculus

Question

Find the derivatives of the functions: $f\left(x\right) = 3^x + {\log }_3 x$

Step-by-Step Solution

Answer

The required answer is $\ln 3 3^x+\frac{1}{x \ln 3}$.

Step 1. Given information.

The given function is: $f\left(x\right) = 3^x + {\log }_3 x$

Step 2. Find the derivative of the given function.

$$\begin{gathered} f\left(x\right) = 3^x + {\log }_3 x \\ f\text{'}\left(x\right) =\frac{d}{dx} \left(3^x + {\log }_3 x\right) \\ =\frac{d}{dx}\left(3^x\right)+\frac{d}{dx}\left({\log }_3 x\right) \\ =\ln 3. 3^x+\frac{1}{x \ln 3} \end{gathered}$$