A 15 foot ladder is resting against the wall. The bottom is initially 10 feet away from the wall and is being pushed towards the wall at a rate of 
  $\frac{1}{4}$  ft/sec. How fast is the top of the ladder moving up the wall 12 seconds after we start pushing?

A tank of water in the shape of a cone is leaking water at a constant rate of  $2\ ft^3$  /hour
. The base radius of the tank is 5 ft and the height of the tank is 14 ft. At what rate is the depth of the water in the tank changing when the depth of the water is 6 ft?

A spherical balloon is inflated so that its volume is increasing at the rate of 20  $ft^3$  /min. How fast is the surface area of the balloon increasing when the radius is 4 feet?

Differentiate the following  $y=x^2\ln\ x+2e^{3x}$  

Differentiate  $y=\left(x\ \tan\ e^x\right)^3$  

Find the  $\frac{dy}{dx}$  for $x^3+y^3=3xy^2$  by using Implicit Differentiation

Using Implicit Differentiation, find  $\frac{\text{d}y}{\text{d}x}$  for  $\sin\ \left(x^2y^2\right)=x$