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Compute the derivative of the given function

Compute the derivative of the function

    \[ f(x) = \frac{\sin^2 x}{\sin (x^2)}. \]


Using the chain rule we compute,

    \begin{align*}   f'(x) &= \frac{(2 \sin x \cos x)(\sin (x^2)) - (\sin^2 x)(2x \cos (x^2))}{\sin^2 (x^2)} \\[8pt]  &= \frac{2 \sin x \big(\cos x \sin (x^2) - x \sin x \cos (x^2)\big)}{\sin^2 (x^2)}  \end{align*}

3 comments

    • RoRi says:

      I think that it’s correct. What do you think the error is? I pulled a 2 \sin x out of both terms. Maybe I should make the parentheses bigger.

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