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    Working with derivatives and tangents

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    1.) Find the derivative of the function:
    a.) f(x) = x + 1/x^2

    b.) f(x) = (2/3rd root of x) + 3 cos x

    2.) Find equation of tangent line to the graph of f at the indicated point:
    a.) y = (x^2 + 2x)(x + 1) ; (1,6)

    © BrainMass Inc. brainmass.com December 24, 2021, 4:47 pm ad1c9bdddf
    https://brainmass.com/math/derivatives/working-derivatives-tangents-7763

    SOLUTION This solution is FREE courtesy of BrainMass!

    1) y = x + (1/x^2)

    dy/dx = 1 + d/dx(x^-2)

    = 1 + [-2 * x^-3]

    = 1 - (2/x^3) Answer

    2)y = [2/x^(1/3)] + 3 Cos(x)

    dy/dx = 2*(-1/3)[x^(-1/3)-1] + 3*-Sin(x)

    = -(2/3)[1/x^(4/3)] - 3 Sin(x)

    remember to include all brackets when you copy it

    we used the relations

    dx^n = n x^n-1

    and d(cosx) = -Sinx

    2) We will find the slope of the tangent at the given point first

    slope = dy/dx

    dy/dx = [d(x^2+2x)](x+1) + (x^2+2x)[d(x+1)] Product rule

    = (2x+2)(x+1) + (x^2+2x)

    Now at the point x=1 the slope is

    =(2+2)(2)+ (4+4) = 8+8 = 16

    Once we have a slope and a point, we can write an equation for a line using the point slope form for a line with slope m at (a,b)
    (y-b) = m(x-a)
    Our equation to the tangent is

    y-6 =16(x-1)

    or, y = 16 x -16 + 6 = 16x - 10

    Please verify the steps.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:47 pm ad1c9bdddf>
    https://brainmass.com/math/derivatives/working-derivatives-tangents-7763

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