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Math Help - Find slope of the tangent line

  1. #1
    Newbie DerekZ10's Avatar
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    Find slope of the tangent line

    Hi, I have no idea where to go for help and am hoping someone here can help me here for this problem.

    The problem is based on sections 5.5(Bases Other than e and Applications)-5.6(Inverse Trigonometric Functions) in Calculus 9th edition by Larson. Chapter 5 is about Logarithmic, Exponential, and Other Transcendental Functions.

    1. Find the slope of the tangent line to the graph of the given function at the given point.

    y = 3x arcsin x , (1/2 , pi/4) Give the slope as an EXACT value, not a decimal approximation.
    I have no idea where to start. Thank you.
    Last edited by DerekZ10; January 29th 2011 at 04:25 PM.
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  2. #2
    Newbie DerekZ10's Avatar
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    Here is what I've done up to this point.

    1. y= (3x)(arcsin(x)) ((1/2),(pi/4))

    Found the derivative using the product rule: (f*g)' = f'*g + f*g'

    Used d/dx (arcsin u) = (u')/(sqrt(1-u^2))

    2. y' = (3)(arcsin(x)) + (3x)((1)/(sqrt(1-x^2)))

    Simplified

    3. y' = 3arcsin(x) + (3x)/(sqrt(1-x^2))

    substituted x with 1/2 to get:

    4. y = pi/2 + Sqrt(3)

    Is pi/2 + sqrt(3) the correct answer?
    Last edited by DerekZ10; January 29th 2011 at 05:29 PM.
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  3. #3
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