Question

y=sin(log(cosx)),Find dy/dx for the given function y wherever defined

Answer 1

y = sin(log(cosx))

differentiate with respect to x,

$\frac{dy}{dx}=\frac{d\{sin(log(cosx))\}}{dx}\\\\=cos(log(cosx))\times\frac{d\{log(cosx)\}}{dx}\\\\=cos(log(cosx)).\frac{1}{cosx}\frac{d(cosx)}{dx}\\\\=cos(log(cosx)\frac{1}{cosx}.(-sinx)\\\\=-cos(log(cos)).\frac{sinx}{cosx}\\\\=-cos(log(cosx)).tanx$

hence, dy/dx = -cos(log(cosx).tanx

Answer 2

HELLO DEAR,



GIVEN:-
Y = sin{log(cosx)}

put log(cosx) = t so, y = sint


therefore, dy/dx = dy/dt × dt/dx

=> dy/dx = cost × (-sinx)/(cosx)

put t = log(cosx)

=> dy/dx = -cos{log(cosx)} × tanx


I HOPE ITS HELP YOU DEAR,
THANKS