Calculus
Derivatives
When \( f(x) = \ln ( x^{13} ) \), what is the value of \( f'(37)? \)
Details and assumptions
\( \ln \) is the logarithm base \( e \), also called the natural logarithm.
If \( f(x) = 4 \ln (e^ {5} x) \), what is the value of \( f'(1) \)?
If \( f(x) = \log_{2}{x} \), what is \( f'(x) \)?
For \(y=6\ln x+9x,\) what is the value of \(x \cdot \frac{dy}{dx} ?\)
If \( f(x) = \log_{3}{(x+2)} \), what is \( f'(x) \)?