What is implicit cos(xy)=1+sin(y) ?

The answer to implicit cos(xy)=1+sin(y) is (dy)/(dx)=-(ysin(xy))/(xsin(xy)+cos(y))

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implicit cos(xy)=1+sin(y)

implicit derivative

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

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

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

\frac{d}{d x} (4 e^{3 x^{2}})

\frac{2 x ^{3} + 5}{4 x ^{2} + 7}

1 + x^{2}

- \frac{1}{4} (x^{- 4} - x^{8})

e^{- \frac{π}{2} t}

What is implicit cos(xy)=1+sin(y) ?
The answer to implicit cos(xy)=1+sin(y) is (dy)/(dx)=-(ysin(xy))/(xsin(xy)+cos(y))