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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

Quotient and Composite Rules

1. a. use quotient rule to find derivative of this function. f(x) = (20+16x-x^2)/(4+x^2). b. Find any stationary points of the function from 1a. An use the first derivative test to see whether they are local maximum or local minimum of f(x). c. what are the maximum and minimum values of the function f(x) at interval [-6,2]

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 Variables

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 of Curves

See the attached file. 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':