Question

the derivative of sinx with respect to logx is​

Answer 1

The derivative of $sinx$ with respect to $logx$ can be written as, $\frac{dsinx}{dlogx}$

Calculate the derivative of $sinx$ with respect to $x$.

       $\frac{dsinx}{dx}=cosx$

Calculate the derivative of $logx$ with respect to $x$.

       $\frac{dlogx}{dx}=\frac{1}{x}$

The derivative of $sinx$ with respect to $logx$.

         $\frac{dsinx}{dlogx}=\frac{dsinx}{dx}\times\frac{dx}{dlogx}\\\frac{dsinx}{dlogx}=\frac{\frac{dsinx}{dx}}{\frac{dlogx}{dx}}\\\frac{dsinx}{dlogx}=\frac{cosx}{\frac{1}{x}}\\\frac{dsinx}{dlogx}=xcosx$