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# find the derivative of e^(tan-1(x))

$\large\begin{array}{l} \textsf{Finding the derivative of}\\\\ \mathsf{f(x)=e^{tan^{-1}(x)}} \end{array}$ $\large\begin{array}{l} \textsf{You can treat f as a composite function:}\\\\ \begin{cases} \mathsf{f=e^u}\\ \mathsf{u=tan^{-1}(x)} \end{cases}\\\\\\ \textsf{Applying the chain rule:}\\\\ \mathsf{\dfrac{df}{dx}=\dfrac{df}{du}\cdot \dfrac{du}{dx}}\\\\ \mathsf{\dfrac{df}{dx}=\dfrac{d}{du}(e^u)\cdot \dfrac{d}{dx}\big[tan^{-1}(x)\big]} \end{array}$ $\large\begin{array}{l} \mathsf{\dfrac{df}{dx}=e^u\cdot \dfrac{1}{1+x^2}}\\\\ \mathsf{\dfrac{df}{dx}=e^{tan^{-1}(x)}\cdot \dfrac{1}{1+x^2}}\\\\\\ \boxed{\begin{array}{c}\mathsf{\dfrac{df}{dx}=\dfrac{e^{tan^{-1}(x)}}{1+x^2}} \end{array}}\qquad\checkmark \end{array}$ If you're having problems understanding this answer, try seeing it through your browser: http://brainly.com/question/2141557 $\large\textsf{I hope it helps.}$