Derivative Rules - Multi Chain Quotient Natural Exponential to Derivative

Question

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

$$f(x) = \frac{\frac{1}{(x - 2)}}{2e^{x}}$$

Accepted Answer

$$f'(x) = \frac{-(x - 2)^{-2}\left(2e^{x}\right) - \frac{1}{(x - 2)}\left(2e^{x}\right)}{\left(2e^{x}\right)^{2}}$$

Answer

$$f'(x) = \frac{\frac{1}{(x - 2)}\left(2e^{x}\right) - -(x - 2)^{-2}\left(2e^{x}\right)}{\left(2e^{x}\right)^{2}}$$

Answer

$$f'(x) = \frac{-(x - 2)^{-2}\left(2e^{x}\right) - \frac{1}{(x - 2)}\left(2e^{x}\right)}{2e^{x}}$$

Answer

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