Question

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

$$f(x) = \frac{e^{x}}{3 \cdot 8^{x}}$$

Accepted Answer

$$f'(x) = \frac{\left(e^{x}\right)\left(3 \cdot 8^{x}\right) - \left(e^{x}\right)\left(3 \cdot 8^{x}\ln{8}\right)}{\left(3 \cdot 8^{x}\right)^{2}}$$

Answer

$$f'(x) = \frac{\left(e^{x}\right)\left(3 \cdot 8^{x}\ln{8}\right) - \left(e^{x}\right)\left(3 \cdot 8^{x}\right)}{\left(3 \cdot 8^{x}\right)^{2}}$$

Answer

$$f'(x) = \frac{\left(e^{x}\right)\left(3 \cdot 8^{x}\right) - \left(e^{x}\right)\left(3 \cdot 8^{x}\ln{8}\right)}{3 \cdot 8^{x}}$$

Answer

$$f'(x) = \frac{\left(e^{x}\right)\left(3 \cdot 8^{x}\right) + \left(e^{x}\right)\left(3 \cdot 8^{x}\ln{8}\right)}{\left(3 \cdot 8^{x}\right)^{2}}$$

Derivative Rules - Multi Quotient Natural and General Exponential to Derivative