Question

Find the derivative f'(x) using the chain, natural exponential, and general exponential rules.

$$\begin{array}{l} \displaystyle \frac{d}{dx}e^{x} = e^{x} \[12pt] \displaystyle f(x) = \sqrt[3]{(3e^{x} + 2 \cdot 9^{x})} \end{array}$$

Accepted Answer

$$f'(x) = \frac{1}{3}(3e^{x} + 2 \cdot 9^{x})^{-\frac{2}{3}} \cdot \left(3e^{x} + 2 \cdot 9^{x}\ln{9}\right)$$

Answer

$$f'(x) = \frac{1}{3}(3e^{x} + 2 \cdot 9^{x})^{-\frac{2}{3}}$$

Answer

$$f'(x) = (3e^{x} + 2 \cdot 9^{x})^{-\frac{2}{3}} \cdot \left(3e^{x} + 2 \cdot 9^{x}\ln{9}\right)$$

Answer

$$f'(x) = \frac{1}{3}(3e^{x} + 2 \cdot 9^{x})^{\frac{1}{3}} \cdot \left(3e^{x} + 2 \cdot 9^{x}\ln{9}\right)$$

Derivative Rules - Multi Chain Natural and General Exponential (with Rule) to Derivative