Overview
1. Given [Image unavailable: LaTeX: f\left(x\right)=\frac{1}{2x+7}], find [Image unavailable: LaTeX: f'\left(a\right)]using the difference quotient.
2. Find an equation of the line tangent to the function in number 1 at [Image unavailable: LaTeX: a=-2].
3. Given [Image unavailable: LaTeX: f\left(x\right)=-7x^5+2\ln x-x^{\frac{1}{3}}] find [Image unavailable: LaTeX: f'\left(x\right)and\:f''\left(x\right)].
4. Given [Image unavailable: LaTeX: f\left(x\right)=\frac{x+1}{x^2e^x}] find [Image unavailable: LaTeX: f'\left(x\right)].
5. Find [Image unavailable: LaTeX: \lim_{x\longrightarrow0}\frac{7x}{\sin6x}]
6. Given [Image unavailable: LaTeX: f\left(x\right)=\tan\left(e^x\sqrt[]{x}\right)], find [Image unavailable: LaTeX: f'\left(x\right)].
7. Use implicit differentiation to find [Image unavailable: LaTeX: \frac{dy}{dx}]. [Image unavailable: LaTeX: \sqrt[]{x+y^2}=\sin y]
8. At noon, a city park manager starts filling a swimming pool. If [Image unavailable: LaTeX: V\left(t\right)]V ( t )is the volume of water ( in [Image unavailable: LaTeX: ft^3]) in the swimming pool [Image unavailable: LaTeX: t] hours after noon, then what does [Image unavailable: LaTeX: \frac{dV}{dt}] represent?