AP Calculus AB Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

Let $f(x)=\arcsin (x)$. Using the derivative of an inverse function, find $f^{\prime }(1/2)$.

If $y={\cos }^3(x^2)$, find $\frac{dy}{dx}$.

If $f$ is a differentiable function and $g(x)=[f(x){]}^3$, find $g^{\prime }(2)$ given that $f(2)=-2$ and $f^{\prime }(2)=5$.

Differentiate $y=\ln (x^4+7)$ with respect to $x$.

If $y=\arctan (2x)$, what is $\frac{dy}{dx}$?

Find $\frac{dy}{dx}$ if $y=x^2\sin (3x)$.

Find $\frac{dy}{dx}$ if $y=(3x^2+1{)}^5$.

If $f(x)=e^{\sin x}$, find $f^{\prime }(x)$.

Find $\frac{dy}{dx}$ by implicit differentiation: $x^3+y^3=6xy$.

Find $\frac{d}{dx}[\ln (\sin x)]$.

Differentiate $y={\tan }^{-1}\left(\frac{x}{3}\right)$ with respect to $x$.

Use implicit differentiation to find $\frac{dy}{dx}$ for $x^2+y^2=25$.