Calculus 1: Exponential and Logarithmic Functions

Determine the slope of the tangent line to the function $f(x) = 2e^{-3x}$at $(0,2)$

For the following problem, find the derivative of $f(x) = 5^{x^{3} - 4}$

Use the properties of logarithms to show that the derivative of $\log_{a}x = \frac{1}{(\ln{a})x}$

Use implicit differentiation to show that the derivative of $\ln{x} = \frac{1}{x}$ for $x > 0$

Note that many classes introduce logarithmic differentiation before implicit differentiation.

Find the derivative of $f(x) = \frac{\ln{(2x)}}{x^4}$