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Compute the derivative of the given function

Compute the derivative of the function

    \[ f(x) = \frac{x}{\sqrt{4-x^2}}. \]


Using the chain rule we compute,

    \begin{align*}   f'(x) &= \frac{\sqrt{4-x^2} - x \left(\frac{1}{2}\right) (-2x)(4-x^2)^{-\frac{1}{2}}}{4-x^2} \\[8pt]  &= \frac{4-x^2+x^2}{(4-x^2)^{\frac{3}{2}}} \\[8pt]  &= \frac{4}{(4-x^2)^{\frac{3}{2}}}.  \end{align*}

2 comments

  1. 123456grimmjaw says:

    Where did the root of the first term going from the first to the second step go? I cant seem to figure it out

    Hope you can help me ….

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