### Derivative of Hyperbolic Function

G(x)= ln(cosh x)

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G(x)= ln(cosh x)

Y= x/(e^x +1)

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 see the attached file for the fully formatted problems.

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

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

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).

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

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

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

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

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

(See attached file for full problem description) The derivative of the constant function f(x) = c is _________.

Find the first three derivatives of the function f(x) = 2cos x sin 2x. (See attached file for full problem description)

Calculus - Chain Rule. Finding Derivatives using Chain Rule. See attached file for full problem description.

Please see the attached file for the fully formatted problems.

Find the three partial derivatives of f(x,y). See attached file.

Second Derivative. See attached file for full problem description.

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).