I need to find dydx: d/(dx)e^ycosx=1+sin(xy) using implicit differentiation.

Talia Frederick

Talia Frederick

Answered question

2022-11-23

I need to find d y d x :
d d x e y cos x = 1 + sin ( x y )
using implicit differentiation.
So far I've gotten to this point which I don't think I'm doing right because then I get stuck:
e y ( sin x ) + ( cos x ) ( e y ) ( d y d x ) = cos ( x y ) ( x ) ( d y d x ) + y ( 1 )
Am I right? Am I wrong? If I'm right I definitely have no clue where to go...and if I'm wrong...then again I have no idea what to do.

Answer & Explanation

Melanie Lam

Melanie Lam

Beginner2022-11-24Added 12 answers

e y cos x = 1 + sin x y e y y cos x e y sin x = cos x y ( y + x y ) y ( e y cos x x cos x y ) = y cos x y + e x sin x y = y cos x y + e x sin x e y cos x x cos x y
Bo Walls

Bo Walls

Beginner2022-11-25Added 1 answers

e y cos x = 1 + sin ( x y )
e y y cos x sin x e y = cos ( x y ) ( y + x y )

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