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Math Help - differentiation

  1. #1
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    Post differentiation

    Use logarithmic differentiation to find the derivative of the following function:
    y
    = (x^3 + 1/(sin^2(x) (x^5x^2)^7))^(1/4)

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    Quote Originally Posted by Sally_Math View Post
    Use logarithmic differentiation to find the derivative of the following function:
    y
    = (x^3 + 1/(sin^2(x) (x^5x^2)^7))^(1/4)

    y = \left[\frac{x^3+1}{\sin^2{x} \cdot (x^5-x^2)^7}\right]^{\frac{1}{4}}

    this more of an algebra drill than it is an exercise in derivatives. use the laws of logs to break down the expression ...

    \ln{y} = \frac{1}{4}\left[\ln(x^3+1) - 2\ln(\sin{x}) - 7\ln(x^5-x^2)\right]

    now take the derivative ...

    \frac{y'}{y} = \frac{1}{4}\left[\frac{3x^2}{x^3+1} - 2\cot{x} - \frac{7(5x^4-2x)}{x^5-x^2}\right]<br />

    finish up by multiplying both sides by y
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