# MATH 2301-102 and -103 Fall 2017 Calculus I Recitation 7 Week 8

See the coversheet for instructions and the point value of each problem.

1. Prove that $$\displaystyle \frac{d}{dx} \left(\cot^{-1}(x)\right) = -\frac{1}{1+x^2}$$.
2. A ladder $$10\,\mathrm{ft}$$ long leans against a vertical wall. It starts slipping, and the bottom of the ladder slides away from the base of the wall at a speed of $$2\,\mathrm{ft/s}$$.
1. Draw and label a diagram illustrating this scenario.
2. How fast is the angle between the ladder and the wall changing when the bottom of the ladder is $$6\,\mathrm{ft}$$ from the base of the wall?
3. Show that $$\displaystyle \cosh(x)-\sinh(x)=e^{-x}$$.
4. Use logarithmic differentiation to find the derivative of $y=\left(\left(\tan^{-1}(\log_2(x))\right)^{\sinh(x^2)}\right)\csc(3^x) \,.$