What is implicit sin(5x+6y)=xy ?

The answer to implicit sin(5x+6y)=xy is (dy)/(dx)=(y-5cos(5x+6y))/(6cos(5x+6y)-x)

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implicit sin(5x+6y)=xy

implicit derivative

sin (5 x + 6 y) = x y

\frac{d y}{d x} = \frac{y - 5 cos ( 5 x + 6 y )}{6 cos ( 5 x + 6 y ) - x}

Solution steps

sin (5 x + 6 y) = x y

Treat

y

y (x)

Differentiate both sides:

cos (5 x + 6 y) (5 + 6 \frac{d y}{d x}) = y + x \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{y - 5 cos ( 5 x + 6 y )}{6 cos ( 5 x + 6 y ) - x}

\frac{d y}{d x} = \frac{y - 5 cos ( 5 x + 6 y )}{6 cos ( 5 x + 6 y ) - x}

\frac{d ^{2} y}{d x ^{2}} = 9 y

\frac{d}{d x} (- 4 \cdot sin^{2} (x) + 4 \cdot sin^{2} (x + \frac{π}{3}))

\frac{d}{d x} (arcsin (x^{2} - 1))

f (x) = 0.6831 x^{- 1.031}, at x = 1

\frac{d ^{2} x}{d t ^{2}} + 5 \frac{d x}{d t} + 6 x = 2 e^{- 3 t}

What is implicit sin(5x+6y)=xy ?
The answer to implicit sin(5x+6y)=xy is (dy)/(dx)=(y-5cos(5x+6y))/(6cos(5x+6y)-x)