Question

find the derivative of sinx with respect to logx​

Answer 1

Step-by-step explanation:

differentiate both separately and then divide

Answer 2

To find :

Derivative of sin x with respect to log x .

Explanation :

For ease in calculation , we first derivate sin x with respect to x , and then log x with respect to x ,

After calculating this , divide both results.

Step 1 ,

Let y = sin x

then , $\frac{dy}{dx}$ = $\frac{d(sin x)}{dx}$

we know derivative of sin x = cos x

therefore , $\frac{d(sin x)}{dx}$ = cos x

Step 2 ,

Now , let p = log x

then , $\frac{dp}{dx}$ = $\frac{d(log x)}{dx}$

we know , derivative of log x with respect to x = $\frac{1}{x}$

therefore , $\frac{d(log x)}{dx}$ = $\frac{1}{x}$

Step 3,

Derivative of sin x with respect to log x ($\frac{dy}{dp}$) = $\frac{cos x}{\frac{1}{x} }$

                                                                         = x cosx

Final answer

Hence , the derivative of sin x with respect to log x = x cosx