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Derivatives

How fast is the brick falling after 2 seconds have passed?

A brick comes loose from near the top of a building and falls such that its distance s (in feet) from the street (after t seconds) is given by the equation s(t) = 200 - 16t^2 (see equation in attached file) How fast is the brick falling after 2 seconds have passed?

Finding Derivatives (12 Problems)

Answers and working to the questions: 1. Obtain dy for the following expressions. dx (a) y = (5x + 4)3 (b) y = (3 - 2x)5 (c) y = square root (5 - 0.6x) (d) y = (2 + 3x)-0.6 2. Differentiate the following with respect to o. (a) f(o) = sin(5o - 2) (b) f(o) = cos(4 - 3o) (c)

Derivatives and Rate of Change

1: Both forms of the definitions of the derivative of a function f at number a. 2: A 13ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of 2ft/sec how fast will the foot of the ladder be moving away from the wall when the top is 5ft above the ground? 3: y': X^2 - 2XY + Y^3 = C

Derivatives

Given f(x)=(x^2+3*x+1)^5 / (x+3)^5 , identify a function u of x and an integer n not equal to 1 such that f(x)=u^n. Then compute f'(x).

Derivatives

Write down the derivative of each of the following functions. f(x)=e^-2x. (thats e to the power minus2x). g(x)=sin(7x). Hence by using the product rule,differtiate k(x)=e^-2xsin(7x)

Determine derivative

(See attached file for full problem description) Determine the derivative: 1) d/dx

Differentiation of composite function - integral form

(See attached file for full problem description with proper symbols) --- Assume that f is continuous on [a,b], g is differentiable on [c,d], g([c,d]) [a,b] and F(x) = For each x [c,d]. Prove that F'(x)=f(g(x))g'(x) For each x (c,d).

Differentiation

Differentiate: 1) y=2x^2+5x+1 at x=5 2) y=1 - x - x^3 at x=-3 3) y = (1/x^2) - 2x^3 at x = -1

Revenue, Supply and Demand Functions : Derivatives and Integrals

5. A man was sentenced to 50 years in prison when he was 20 years old. While in prison he reflected on his life and decided that he should turn his life around and do something good for his society. He then became a model prisoner and his good behavior earned him the privilege to pursue a career in law. When he became 39 years