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Use the definition of the derivative to find f ' (x) of f (x) = sin xy + cos π y^2
Find f ' (x) of f(x) = x^3 - 3x^2 + 4 / x^2
Find the derivative g(t) = √ 1 / t^2 - 2
Find dy over dx by implicit differentiation of x^3 - 2x^2y + 3xy^2 = 38 and evaluate the derivative at the point (2,3)
Assume that x and y are both differentiable functions of t and find the indicated values of dy over dt and dx over dt of x^2 + y^2 = 25 at a) find dy over dt when x=3, y=4 and dx over dt = 8
A spherical balloon is inflated with gas at the rate of 20 cubic feet per minute. How fast is the radius of the balloon increasing at the instant the radius is 2 feet?
Find the equation of the tangent line and the normal line of y = ^3√ (x-2)^2 at (3,1)
Find the equation of the tangent line of the function f(x) = (x^3 - 3x + 1)(x +2) at the point (1,-3)
A ball is thrown straight down from the top of a 220 foot building with an initial velocity of -22ft/sec. What is the velocity after 3 seconds? (Use standard position equation)
