### Finding Derivatives using the Chain Rule

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

Explore BrainMass

- Anthropology
- Art, Music, and Creative Writing
- Biology
- Business
- Chemistry
- Computer Science
- Drama, Film, and Mass Communication
- Earth Sciences
- Economics
- Education
- Engineering
- English Language and Literature
- Gender Studies
- Health Sciences
- History
- International Development
- Languages
- Law
- Mathematics
- Philosophy
- Physics
- Political Science
- Psychology
- Religious Studies
- Social Work
- Sociology
- Statistics

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

The problem states: Find dw/dt (a) using the appropriate chain rule and (b) by converting w to a function of t before differentiating. w = xy x = s sin t, y = cos t the solution in my solution manual goes like this: a) using the chain rule they come up with: 2y cos t + x(-sin t) = 2y cos t - x sin t = 2

Suppose g is the inverse function of a differentiable function f and let G(x) = 1/g(x), if f(3) = 2 and f'(3) = 1/9, find G'(2). Please see the attached file for the fully formatted problems.

Find (f-1)'(a) (or g'(a)) f(x) = sqrt of (x3 + x2 + x + 1) , a=2

Please answer the attached questions.

1. A college calculus professor wanted to investigate the relationship between student's scores on the first exam and the overall course grades. A sample of the data is below. (All values are given in percents.) first exam score 54 98 73 100 88 90 77 73 81 final grade % 60 93 69 95 82 87 72 71 74

Suppose f=f(x), g=g(x), and I=I(x). Solve the following linear equation to get an implcit solution for I(x): fI' + (f' - g)I = 0 f>0

Calculate the derivative of r(t) = 1/ sqrt 9t^2+5 <3t,1,-2>

Determine the principle unit normal vector of : r(t) = 3ti + 2t^2j

Find the derivative of the function f(x) = (x)(e^-x) My book indicates gives the solution: f'(x) = (x)(e^-x)(-1) + (x^-x)(1) = e^-x(1 - x)

Problem 1 Find the area of the region enclosed by the curves .... Problem 2 Find a formula for the inverse of the function ..... Problem 3 Find (f-1).... Problem 4 Compute the following limits: ..... Problem 5 Find the derivative of the function y = e^x/1+x .

(See attached file for full problem description with proper equations) --- 1, Differentiate f(x) = e(2x + 5) with respect to x 2, Determine f `(t) if f(t) = G(1- e-kt) 3, Determine f ' (y) if f(y) = exp(3 - ¼ y)

I have to understand step by step how to navigate Chapter 3.1 Derivatives of Polynomials and Exponential Functions. However, I don't understand how to get a tangent line from a Y=f (x) if x=a, then use that to find f '(a). I'm given the following: Find equations of the tangent line and normal line to the curve at the give

Initial equation - 100 +10B + 20N - B2 - N2 + 0.5 BN ( B2= B to the secondpower and N2 equals N to the second power) I want to get the first derivative of N so I got this far: 10-2b + .5n =0 .5n=2b -10 N= 4b -20. I can't figure out how they got the answer for N ? Also, why is the number 10 without the B when

Can you please show me how to calculate the following 1. Differentiate f(x) = 1n(5x - 7) with respect to x 2. Obtain the derivative of f(t) = 1n( 5 - 2/3 t)

Differentiate ( find the derivative ) : y=3/(1-X^2)^1/3

Differentiate each of the following functions with respect to the appropriate variable: 1. f(x) = ln(7-5x) 2. y(x)=e^(4x-5) 3. f(x) = ln(x- 3/7 t) 4..... Please see the attached file for the fully formatted problems.

Please show that the function f(x) = ln(x) does not have a relative minimum or relative maximum. Please show that for a polynomial of degree 3, if 1 + i is a zero, then 2 + i is not a zero.

Find the numerical version of each expression 1) sinh 0 2) cosh 0 3) tanh 0 4) tanh1 5) sinh1 6) cosh1 7) sech 0 8) sinh(ln 2) 9) cosh(ln3) 10) cosh^-1 1 11) sinh^-1 1 Use definitions of hyperbolic functions to find each. 1) lim as x approached infinity tanh x 2) lim as x approached infinity sinh x 3) lim a

Please see problems and show step by step solution in detail please. --- 7.4 Inverse functions Differentiate the problems: 1) f(x) = ln(x^2 + 10) 2) f(à?) = ln(cos à?) 3) f(x) =log2(1-3x) 4) f(x) = 5thROOT(ln x) 5) f(x)=SQRTx * (ln x) 6) f(t) = ln [(2t+1)^3 / (3t-1)^4] 7) h(x)=ln(x + SQRT(x^2-1)) 8) g(x)=ln[(

(x-3)^2 / [(x^2)+1] ^2

1.) compute the derivative of f(x)= arctan (x^2) 2.) compute the derivative of f(x)= ln(x^2/(2+x)) 3.) determine an equation for the line tangent to the graph of y= xe^x at the point on the graph were x=2

F'(y) if f(y)=exp ( 3 - 1/4 y )