Fundamentals of Differentiation

What is the derivative of $f(x) = \ln(e^{2x})$?

If the function $f(x) = e^{kx}$ has a derivative of $3e^{2x}$ at $x = 1$, what is the value of the constant $k$?

What is the derivative of $f(x) = \ln x$?

Given that $\frac{d}{dx}[e^{g(x)}] = e^{g(x)} \cdot g'(x)$, what is $\frac{d}{dx}[e^{-2x}]$?

What does it mean if the derivative of a function at a point is exactly 0?

For which value of x does the first derivative of the function defined by $f(x)=\ln(x+4)$ equal one-half?

What is the derivative of $f(x) = \ln(\cos x)$?

If $f(x) = e^x$, what is the value of $f''(x)$?

Consider the differential equation $\frac{dy}{dx}=y \sin(x)$. If $y(0)=e$ and we know $y'(0)=1$, what does this imply about $\frac{dy}{dx}$ evaluated at some point ($a$, $e$)?

What's the second derivative of $\ln(\cos x)$ with respect to x at $\pi/4$?