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Math Help - chain rule derivs.

  1. #1
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    chain rule derivs.

    f() = ln(sin(8))

    h(w) = w^3 ln(14w)

    can someone show me how to do these...much thanks...

    mathaction
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  2. #2
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    Quote Originally Posted by mathaction View Post
    f() = ln(sin(8))

    h(w) = w^3 ln(14w)

    can someone show me how to do these...much thanks...

    mathaction
    hi,

    use chain rule:

    f'(\alpha)=\frac1{\sin(8 \alpha)} \cdot \cos(8 \alpha) \cdot 8 = \frac{8 \cdot \cos(8 \alpha)}{\sin(8 \alpha)} = \frac8{\tan(8\alpha)}

    use product rule and chain rule:

    h'(w)=\ln(14w) \cdot 3 \cdot w^2 + w^3 \cdot \frac1{14w} \cdot 14 = w^2\left(3 \cdot \ln(14w) + 1  \right)
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