Question

Differenciate e^sinx with respect to cos x.

Answer 1

`DIFFERENTIATION \\ \\ \\ Let \: u \: = \: {e}^( \sin(x) ) \: \: and \: v = \cos(x) \\ \\ Then \: , \: (du)/(dx) \: = \: \cos(x) . {e}^( \sin(x) ) \\ \\ and \: \: \: \: \: \: (dv)/(dx) \: \: = \: - \sin(x) \\ \\ \\ Therefore \: , \\ \\ \\ (du)/(dv) \: = \: ( (du)/(dx) )/( (dv)/(dx) ) \: = \: \frac{ \cos(x) . {e}^( \sin(x) ) }{ - \sin(x) } \\ \\ \\ (du)/(dv) \: = \: - \cot(x) . {e}^( \sin(x) ) \: \: \: \: \: \: \: \: \: \: Ans.`