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

Question

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

$$\begin{array}{l} \displaystyle \text{if } h(x) = \frac{f(x)}{g(x)},\ h'(x) = \frac{f'(x)\,g(x) - f(x)\,g'(x)}{[g(x)]^{2}} \[12pt] \displaystyle f(x) = \frac{4e^{x}}{2 \cdot 4^{x}} \end{array}$$

Accepted Answer

$$f'(x) = \frac{\left(4e^{x}\right)\left(2 \cdot 4^{x}\right) - \left(4e^{x}\right)\left(2 \cdot 4^{x}\ln{4}\right)}{\left(2 \cdot 4^{x}\right)^{2}}$$

Answer

$$f'(x) = \frac{\left(4e^{x}\right)\left(2 \cdot 4^{x}\right) - \left(4e^{x}\right)\left(2 \cdot 4^{x}\ln{4}\right)}{2 \cdot 4^{x}}$$

Answer

$$f'(x) = \frac{\left(4e^{x}\right)\left(2 \cdot 4^{x}\right) + \left(4e^{x}\right)\left(2 \cdot 4^{x}\ln{4}\right)}{\left(2 \cdot 4^{x}\right)^{2}}$$

Answer

$$f'(x) = \frac{\left(4e^{x}\right)\left(2 \cdot 4^{x}\ln{4}\right) - \left(4e^{x}\right)\left(2 \cdot 4^{x}\right)}{\left(2 \cdot 4^{x}\right)^{2}}$$

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

Practice:

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