Derivatives of Logarithmic Functions

Derivatives of Logarithmic Functions

Read each question carefully and show all your work. Simplify your answers as much as possible.

1. Find the derivative of the function $f(x) = \ln(x^3 + 2x)$.

2. Differentiate $y = \log_5(4x^2 - 1)$.

3. The derivative of $f(x) = \ln(x)$ is $f'(x) = $  .

4. The derivative of $f(x) = \log_b(x)$ is $f'(x) = $  .

5. Which of the following is the derivative of $f(x) = x^2 \ln(x)$?

6. Find the derivative of $g(x) = \ln(\frac{x^2+1}{x-3})$.

7. The derivative of $f(x) = \ln(e^x)$ is $f'(x) = 1$.