Can anyone help me with the derivative of 5xArctan(2x)???

Thank you!!

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- Mar 9th 2008, 06:57 PMBKennedyDerivative
Can anyone help me with the derivative of 5xArctan(2x)???

Thank you!! - Mar 9th 2008, 07:04 PMTheEmptySet

Use the product rule

let

$\displaystyle f(x)=x$ and $\displaystyle g(x)=\tan^{-1}2x$ then

$\displaystyle f'(x)=1$ and $\displaystyle g'(x)=\frac{2}{1+4x^2}$

by the product rule we get...

$\displaystyle \frac{d}{dx}(fg(x))=f'(x)g(x)+f(x)g'(x)=1 \cdot \tan^{-1}(2x)+x \cdot \frac{2}{1+4x^2}$

Just simplify from there