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

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 $g\text{'}\left(x\right)$.

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?

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

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 $f^{\prime }\left(x\right)$?

Find the derivative of the function $y=1-x^2-x{\cos }^{-1}\left(x\right)$. Which of the following is correct?

Find the gradient vector field of the function $f(x,y)=x{e}^{9xy}$. Which of the following is the correct gradient vector field $\nabla f(x,y)$?