### Finding the Derivatives of a Function

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

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

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

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

Y = ln[(1+ e^x)/(1-e^x)] keywords: natural log

Find the derivative g(t) = e^-3/t^2

Find the derivative : y = x^2e^-x

Find the derivative: y = e^-x^2

Let f′ (x) = √x and f(9) = 19. Find f(x) __ Let f′ (x) = √x and f(9) = 19. Find f(x)

Find the derivative of f(x) = 3 ln x

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]

Two problems are included in attachment.

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?

Let f(x) = e^(0.02x) Find f ′ (2). Round answer to three decimal places.

Y=x^1/3

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.

Find the three second partial derivatives of exp[-{(x-1)^2-(y-1)^2}/2]

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)

Find the derivative of y = (2x)^5

Let f(x) = 1/x Find f"(4). See the attached file.

F(x) = (2x + 1)^1/2

(See attached file for full problem description)

Find the second derivative of f(x) = x4 + 4x3 + x2 + 6x - 1

Please see the attached file for the fully formatted problems.

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':

Use the product rule to find the derivative of y = (x - 7) (x + 4).

F(x)=x^2/(x-1)

Use the product rule to find the derivative of y = (x - 7) (x + 4).

F(x)=(x-2)/(x+1)

Use the product and quotient rules to simplify. All variables represent positive real numbers. principle square root 27/16

4 principle square root 32