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Derivatives and Rates of Change

After t years, the value of a car purchased for V(t) = 20,000(3/4)^t (a) use a graphing utility to graph the function and determine the value of the car 2 years after it was purchased. (b) Find the rates of change of V with respect to t when t = 1 and t - 4. (c) free hand stetch graph of V'(t) and determine the horizont


Please find the derivative of the function. y= 6^(-2x)

Maximum Values by Partial Differentiation

Need some help finding the max value of a multi-variable function as follows exp ^2x - 2x-2y^2+y and the second one is -(2-x)^2y^2-y I am confused as to how to take the partials with the exponential in the first problem and with the - sign outside the parenthesis in the second problem. If you can work out the

Chain rule?

Please explain chain rule i'm a visual person please show several examples

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

Y =c/(1+ y/x^2)^1/2 a is a variable x is a variable c is a constant y is a constant I need to differentiate a with respect to x. Please see the attached file for the fully formatted problems.

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


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).