Question Number 149252 by holomata last updated on 04/Aug/21

e^y =(sin x)(cos x) find (dy/dx)

Answered by Mokmokhi last updated on 04/Aug/21

(dy/dx)=2cot 2x

Answered by physicstutes last updated on 04/Aug/21

e^y (dy/dx) = sin x . (−sinx) + (cos x)(cos x) ⇒ e^y (dy/dx) = cos 2x (dy/dx)=((cos 2x)/e^y )

Commented byMokmokhi last updated on 04/Aug/21

please note that e^y can be presented in terms of x.

Answered by puissant last updated on 04/Aug/21

⇒ y=ln((1/2)(sin(2x))) (dy/dx)=((cos(2x))/((1/2)sin(2x))) = 2((cos(2x))/(sin(2x))) ⇒ (dy/dx) = 2cotan(2x)..

Answered by mathmax by abdo last updated on 04/Aug/21

e^(y ) =sinx.cosx ⇒e^y =(1/2)sin(2x) ⇒y=ln(((sin(2x))/2)) =ln(sin(2x))−ln2 ⇒(dy/dx)=((2cos(2x))/(sin(2x)))=2cotan(2x)