Suppose the figure above shows the graph of $f^{\prime }$, the derivative of a function $f$. At which of the following $x$-values does $f$ have a local maximum?

What is the derivative of the function $f\left(x\right)=e^{4x}$ with respect to $x$?

Find the derivative of the function: $y=e^{tan\left(x\right)}$.

If $f\left(x\right)={(2x^2+5)}^7$, then which of the following is $f^{\prime }\left(x\right)$?

Given the function $g\left(x\right)={\sinh \left(x\right)}^2$, find its derivative $g\text{'}\left(x\right)$.

Differentiate the function $h\left(u\right)=(u-u^2)(u+u^2)$ with respect to $u$.

Given that $3x-tany=4$, what is $\frac{dy}{dx}$ in terms of $y$?

Suppose the function $f\left(x\right)$ has the derivative $f^{\prime }\left(x\right)=3x^2-4x+2$. Find the values of $f^{\prime }\left(1\right)$ and $f^{\prime }\left(2\right)$.

Given the graph of a function $f\left(x\right)$, which of the following statements best describes the graph of its derivative $f^{\prime }\left(x\right)$?