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Math Help - Derivative Help Please

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    Question Derivative Help Please

    Find dy/dx when: y = e * ln (1/x + 1/(x^3) ) Thanks!
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    Re: Derivative Help Please

    \displaystyle \begin{align*} y &= e\ln{\left( \frac{1}{x} + \frac{1}{x^3} \right) } \\ &= e\ln{\left[ \frac{x^2 + 1}{x^3} \right] } \\ &= e\left[ \ln{ \left( x^2 + 1 \right) } - \ln{ \left( x^3 \right) } \right] \\ &= e \left[ \ln{ \left( x^2 + 1 \right) } - 3\ln{(x)} \right] \\ \frac{dy}{dx} &= e \left( \frac{2x}{x^2 + 1} - \frac{3}{x} \right) \end{align*}
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