Unit 2A Practice Exam A

Use the limit definition to find the derivative of $f(x)=x^2+3x$ at $x=1$.

Find the tangent and normal lines to $y=1/x$ at $x=2$.

Differentiate $4x^{7/3}-5x^{-2}$.

Differentiate $(x^2+1)^4e^x$.

Differentiate $\ln(1+\sin^2x)$.

Differentiate $[\tan(1+x^2)]^5/(x^3+1)$.

Find $dy/dx$ for $x^2+xy+2y^2=10$.

Find the tangent line to $y=\arcsin(x/2)$ at $x=1$.

If $g=f^{-1}$, $f(2)=5$, and $f'(2)=-3$, find $g'(5)$.

Use logarithmic differentiation to differentiate $(x^2+1)^{e^x}$.

Find the first four derivatives of $x^4-3x^3+2x$.

Explain why differentiability at $a$ implies continuity at $a$, but continuity does not imply differentiability.

A response model is $R(d)=100d/(d+12)$. Find $R'(d)$ and interpret $R'(12)$.

Write a rule-selection explanation, without computing, for $y=e^{\sin(x^2)}(x+1)^3$.