Math 125I Winter 2003 Name:

Quiz Section:

Derivative Skills Review

2 POINTS EACH – NO PARTIAL CREDIT – NO CALCULATORS 1. Find \frac{dy}{dt} if y = ln(t) sin^{−1}(t)

2. Let g(y) = \frac{tan y}{2y^{3} − y}. Compute g′(y).

3. Find the slope of the tangent line to the curve y = e^{\sqrt{x^{2}+3}} at the point (1, e^{2}).

(over)

4. Suppose f′(x) = 8x^{3} − 5x^{2} + 7 and f(−1) = 2. Find a formula for f(x).

5. Find the general form of the anti-derivative of the function h(t) = \frac{5}{t} + sec(t) tan(t).