AP Calculus AB Unit 2: Differentiation: Definition and Fundamental Properties

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

If $f$ is differentiable at $x=a$, then $f$ is:

Use the limit definition of the derivative to find $f^{\prime }(2)$ for $f(x)=x^2+1$.

Find $f^{\prime }(x)$ if $f(x)=e^x\cos x$.

Find $\frac{d}{dx}\left[\frac{x^2}{x+1}\right]$.

Find the derivative of $f(x)=5x^3-4x^2+7x-2$.

Find the equation of the tangent line to $f(x)=x^2$ at $x=3$.

If the position of a particle is $s(t)=t^3-6t^2+9t$ (in meters, $t$ in seconds), what is its velocity at $t=2$?