listed in the picture

1. Given LaTeX: fleft(xright)=frac{1}{2x+7}, find LaTeX: f'left(aright)using the difference quotient.

2. Find an equation of the line tangent to the function in number 1 at LaTeX: a=-2.

3. Given LaTeX: fleft(xright)=-7x^5+2ln x-x^{frac{1}{3}} find LaTeX: f'left(xright)and:f''left(xright).

4. Given LaTeX: fleft(xright)=frac{x+1}{x^2e^x} find LaTeX: f'left(xright).

5. Find LaTeX: lim_{xlongrightarrow0}frac{7x}{sin6x}




6. Given LaTeX: fleft(xright)=tanleft(e^xsqrt[]{x}right), find LaTeX: f'left(xright).

7. Use implicit differentiation to find LaTeX: frac{dy}{dx}. LaTeX: sqrt[]{x+y^2}=sin y

8. At noon, a city park manager starts filling a swimming pool. If LaTeX: Vleft(tright)
V


(


t


)

is the volume of water ( in LaTeX: ft^3) in the swimming pool LaTeX: t hours after noon, then what does LaTeX: frac{dV}{dt}

represent?

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