What is implicit sin(xy)=cos(x+y) ?

The answer to implicit sin(xy)=cos(x+y) is (dy)/(dx)=(-sin(x+y)-ycos(xy))/(xcos(xy)+sin(x+y))

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implicit sin(xy)=cos(x+y)

implicit derivative

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

\frac{d y}{d x} = \frac{- sin ( x + y ) - y cos ( x y )}{x cos ( x y ) + sin ( x + y )}

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

cos (x y) (y + x \frac{d y}{d x}) = - sin (x + y) (1 + \frac{d y}{d x})

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- sin ( x + y ) - y cos ( x y )}{x cos ( x y ) + sin ( x + y )}

\frac{d y}{d x} = \frac{- sin ( x + y ) - y cos ( x y )}{x cos ( x y ) + sin ( x + y )}

\frac{( 1 0 ^{x} )}{ln ( 10 )}

\frac{\partial}{\partial x} (20 - 4 x^{2} - 3 y^{2})

\int 29 x^{2} ln (x) d x

\frac{d ^{2}}{d x ^{2}} (e^{5 x})

What is implicit sin(xy)=cos(x+y) ?
The answer to implicit sin(xy)=cos(x+y) is (dy)/(dx)=(-sin(x+y)-ycos(xy))/(xcos(xy)+sin(x+y))