### Finding derivative of a rational function using Chain rule or determining du/dx of a rational function

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

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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

How does one use differentials to estimate e raised to some exponent, leaving the answer in terms of e?

We've got a cylindrical can with height =h and radius =r. It will hold 4L (4,000 cm cubed) of some liquid. The material for the top and bottom costs 2 cents per square cm and the material for the side costs 1 cent per square cm. Find h and r to minimize the cost. keywords: derivative, differentiation, differentiate, mini

1) Find the absolute maximum and the absolute minimum of F(x)= (x+2)/(x-2) on intervals [- 4,4]. 2) Find the derivative of the following: a- F(x)= e^(2x) x^2 + e^(-x^2) b- F(x)= ln(x^3 - 3)^4 3) Use the logarithmic differentiation to find the derivative of : Y= √(4+3x^2)/(x^2+1)^(1/3) ---

Where is the graph of 1/4x^4 - 2x^2 concave down? keywords: concave-down, concave-up, up, second-derivatives, second, derivatives

Consider this equation: x2 - 2xy + 4y2 = 64 A) write an expression for the slope of the curve at any point (x,y) B) Find the equation of the tangent lines to the curve at the point x = 2 C) find d2y/dx2 at (0,4)

F(x) = (1 + 2³)^12 g(z) = -3 4(z^5 +2z - 5)^4

The function has one critical number. Find it. A student decided to depart from Earth after his graduation to find work on Mars. Before building a shuttle, he conducted careful calculations. A model for the velocity of the shuttle, from liftoff at t = 0 s until the solid rocket boosters were jettisoned at t = 60.7 s, is gi

A street light is at the top of a 14 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole? Note: You should draw a picture of a right triangle with the vertical side representing the pole,

1, Obtain the derivative of f(t) 1n(5-(2/3)t) f(t) = 1n (-2/3t)+5 2, Determine f ′ (t) if f(t) = G(1 - e-kt) = G - Ge-kt

A person's fortune increases at a rate to the square of they're present wealth. If the person had one million dollars a year ago and has two million today then how much will the person be worth in six months?

Use implicit differentiation to find the slope of the tangent line to the curve at the point . Find by implicit differentiation. Match the expressions defining implicitly with the letters labeling the expressions for . 1. 2. 3. 4. A. B. C. D. Let Let Let Then

Prove : (dy/dθ)^2 + (dx/dθ) = r^2 + (dr/dθ)^2

Consider the function f(x,y,z) = (e^z)ln(x^2 + y^2) a) Is there a vector r such that the directional derivative of f at (1,1,0) in the direction of r equals 1? If there is, find one such vector. If not, explain why not. b) Is there a vector r such the directional derivative of f at (1,1,0) in the direction of r equals to