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## Derivatives

A derivative is simply a rate of change. Whether you're modeling the movement of a particle or a supply/demand model, this is a key instrument of Calculus.

# Logarithmic Functions

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 $$f'(x)$$?

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