### Find derivative

Two problems are included in attachment.

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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?

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).

Implicit Differentiation. See attached file for full problem description.

Find dy/dx if 3x + 4y -5 = 0 using implicit differentiation.

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)

See the attached file for full problem description. Assume that f, f' and f''' are continuous on [a,b] and f(a)=f(b)=0. Then S b--> a f(x)f''(x)dx = -S b--> a (f'(x))^2 dx

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

(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).

1) Determine the derivative function f' from the definition Involving x+ x 2)Determine the differential of f f(x)=1/(x+4), x keywords: derivatives, differentials

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1. Findthe point ofinfiection of the function describedby f(x)= x3- 6x2+12x- 4. Apply an appropriate test to mate sure it is a point of inflection you found. 2. A large cube of ice is melting so that its volume, V. is decreasing at the rate of 60 cm3/s. Find the rate at which each side, x, of the cube is decreasing at the momen

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

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

1. The table below presents the net sales (Revenue), R(t) in billions of dollars for Wal-Mart for the period 1994 to 2004 (Wal-Mart's website). Let t = 0 represent 1990. t 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 P(t) 63 78 89 100 112 131 156 181 204 230 256 a. Use your graphing utility to find the reg