Calculus 1 Worksheet - Part 2 5. More Derivatives: a) Compute the derivative of the function y=1x+xy=x1+x . b) Find the second derivative of the function f(x)=2x3−5x2+3x−7f(x)=2x3−5x2+3x−7. 6. Applications of Integrals: a) Given the velocity function v(t)=2t−3v(t)=2t−3, find the displacement of an object from t=1t=1 to t=4t=4. b) The rate of change of the area of a circle with respect to its radius is 6π cm2/cm6πcm2/cm. Find the area of the circle when the radius is 4 cm4cm. 7. Exponential and Logarithmic Functions: a) Differentiate the function y=e2x+ln(x)y=e2x+ln(x). b) Evaluate the following limit: limx→0+xln(x)x→0+limxln(x) 8. Related Rates: A ladder, 10 feet long, is leaning against a wall. The bottom of the ladder is pulled away from the wall at a rate of 2 feet per second. How fast is the top of the ladder moving down the wall when the bottom of the ladder is 6 feet away from the wall?
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