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    Derivatives

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    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

    See the attached file. 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 Solution

    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

    First Derivative Test and Maximizing Revenue Functions

    Using the first derivative test, find the critical values and intervals where the function is increasing. y = x^2 - 6x + 2 Using the first derivative test, find the critical values and intervals where the function is increasing. y = x^3 - 27x + 2 If the demand function is given by p = - 0.4x + 24, find the value at

    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 Proper Equations

    (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

    get the first derivative of N

    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 Calculation Functions

    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)

    Derivatives of Logarithmic and Exponential Problems

    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.

    Derivatives: Relative Minimum or Maximum

    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.

    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

    Derivatives, maxima, minima

    1. Find the derivative: f(x) = (x^3-8)^(2/3) 2. Write and equation of the tangent line to the graph of y = f(x) at the point on the graph where x has the indicated value. f(x) = (3x^2 + 5x + 4)(4x + 3), x=0 3. Find the values of any relative extrema: f(x)=1/(x^2-1)