How to differentiate e^y cos(x)=6+sin(xy)?

Charles Foster

Charles Foster

Answered question

2023-02-11

How to differentiate e y cos ( x ) = 6 + sin ( x y ) ?

Answer & Explanation

Malachi Weber

Malachi Weber

Beginner2023-02-12Added 5 answers

Here,
e y cos x = 6 + sin ( x y )
Diff.w.r.t. x , using product and chain rule
e y d d x ( cos x ) + cos x d d x ( e y ) = 0 + cos ( x y ) d d x ( x y )
e y ( - sin x ) + cos x ( e y d y d x ) = cos ( x y ) [ x d y d x + y 1 ]
- e y sin x + e y cos x d y d x = x cos ( x y ) d y d x + y cos ( x y )
e y cos x d y d x - x cos ( x y ) d y d x = e y sin x + y cos ( x y )
d y d x [ e y cos x - x cos ( x y ) ] = e y sin x + y cos ( x y )
d y d x = e y sin x + y cos ( x y ) e y cos x - x cos ( x y )

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