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

Question

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

$$\begin{array}{l} \displaystyle \frac{d}{dx}a^{x} = a^{x}\ln a \[12pt] \displaystyle f(x) = \frac{1}{(2e^{x} + 5 \cdot 2^{x})^{2}} \end{array}$$

Accepted Answer

$$f'(x) = -2(2e^{x} + 5 \cdot 2^{x})^{-3} \cdot \left(2e^{x} + 5 \cdot 2^{x}\ln{2}\right)$$

Answer

$$f'(x) = (2e^{x} + 5 \cdot 2^{x})^{-3} \cdot \left(2e^{x} + 5 \cdot 2^{x}\ln{2}\right)$$

Answer

$$f'(x) = -2(2e^{x} + 5 \cdot 2^{x})^{-2} \cdot \left(2e^{x} + 5 \cdot 2^{x}\ln{2}\right)$$

Answer

$$f'(x) = -2(2e^{x} + 5 \cdot 2^{x})^{-3}$$