Evaluate the limit (x-4)/(x^2-x-12) as x approaches 4

Find the slope of (x^2)y=8 at the point (2,2).

. Evaluate the limits of lim (x^3-2x+9) /(2x^3-8).

Determine the slope of the curve y=x^2-3x as it passes through the origin.

A cylindrical boiler is to have a volume of 1340 cu ft. The cost of the metal sheets to make the boiler should be minimum. What should be its diameter in feet?

What is the slope of the tangent to y=(x^2+1)(x^3-4x) at (1,-6)?

What is the derivative with respect to x of (x+1)^3 – x^3.

Find the second derivative of y=2x+3(4x+2)^3 when x=1.

Find dy/dx by implicit differentiation at the point (3,4) when x^2+y^2=25

Find the derivative of y=x^x.