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Derivatives

Critical Numbers, Derivatives and Rates of Change

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

Applications of Derivatives Word Problems and Rate of Change

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,

Interest and applications of derivatives.

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?

Implicit Differentiation

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

Directional Derivatives

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

Partial Differentiation and the Chain rule

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

Derivatives and Inverse Functions

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.

Functions : Linear Regression, Derivatives and Rate of Change

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

Implicit Differentiation

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

Region enclosed by Curves, Inverses, Limits and Derivatives

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 .

Differentiation

(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)

Derivatives of Polynomials and Exponential Functions

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

I need help figuring out this problem.

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

Differentiation

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)

Inverse functions

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[(

Derivative

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