What is implicit 4xy=sin(x+y) ?

The answer to implicit 4xy=sin(x+y) is (dy)/(dx)=(cos(x+y)-4y)/(4x-cos(y+x))

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implicit 4xy=sin(x+y)

implicit derivative

4 x y = sin (x + y)

\frac{d y}{d x} = \frac{cos ( x + y ) - 4 y}{4 x - cos ( y + x )}

Solution steps

4 x y = sin (x + y)

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{cos ( x + y ) - 4 y}{4 x - cos ( y + x )}

\frac{d y}{d x} = \frac{cos ( x + y ) - 4 y}{4 x - cos ( y + x )}

y = x^{2} - 2 x - 4, (2, - 4)

\frac{d}{d x} (1 + sin (2 x))

\int \frac{2 x ^{4} - 2 x ^{2}}{x ^{2}} d x

ln (x + 1 + x^{2})

What is implicit 4xy=sin(x+y) ?
The answer to implicit 4xy=sin(x+y) is (dy)/(dx)=(cos(x+y)-4y)/(4x-cos(y+x))