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Math Help - Pre-Cal: Deriviatives & Graph Line Tangent

  1. #1
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    Pre-Cal: Deriviatives & Graph Line Tangent

    Please can some one help me with these 3 Problems I am lost...
    I Greatly Appreciated!


    Find f(x) and simplify

    f(x) = (x^2-1/ √x)^4

    f(x) = e^-x-1/ e^-x+1

    Find an equation of the line tangent to the graph of
    f(x) = x ln x at x = 1
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  2. #2
    Super Member Aryth's Avatar
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    1) f(x) = \left(\frac{(x^2 -1)}{\sqrt{x}}\right)^4

    1: Distribute the power of 4.

    f(x) = \left(\frac{(x^2 - 1)^4}{\sqrt{x}^4}\right)

    2: Simplify the denominator:

    f(x) = \left(\frac{(x^2 - 1)^4}{x^2}\right)

    3: Use the following rule:

    \frac{d}{dx}\left[\frac{u}{v}\right] = \frac{u'v - vu'}{v^2}

    4: Solve:

    f'(x) = \frac{8x(x^2 - 1)^3*x^2 - (x^2 - 1)^4*2x}{x^4}

    5. Simplify:

    f'(x) = 2x(x^2 - 1)^3\frac{4x^2 - (x^2 - 1)}{x^4}

    f'(x) = 2x(x^2 - 1)^3\frac{3x^2 + 1}{x^4}
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  3. #3
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    ^^^ Thank you

    Can anyone help with the other two problems


    f(x) = e^-x-1/ e^-x+1


    Find an equation of the line tangent to the graph of

    f(x) = x ln x at x = 1
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