What is implicit y=2sin(pix-y) ?

The answer to implicit y=2sin(pix-y) is (dy)/(dx)=(2picos(pix-y))/(1+2cos(-y+pix))

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implicit y=2sin(pix-y)

implicit derivative

y = 2 sin (π x - y)

\frac{d y}{d x} = \frac{2 π cos ( π x - y )}{1 + 2 cos ( - y + π x )}

Solution steps

y = 2 sin (π x - y)

Treat

y

y (x)

Differentiate both sides:

\frac{d y}{d x} = 2 cos (π x - y) (π - \frac{d y}{d x})

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{2 π cos ( π x - y )}{1 + 2 cos ( - y + π x )}

\frac{d y}{d x} = \frac{2 π cos ( π x - y )}{1 + 2 cos ( - y + π x )}

\int_{3}^{- 1} x^{3} d x

x^{^{'}} + 5 x = 6

y = \frac{1}{x - 2}

\int 2 cos (θ) + 2 d θ

\int \frac{1}{49 e ^{- 8 x} + e ^{8 x}} d x

What is implicit y=2sin(pix-y) ?
The answer to implicit y=2sin(pix-y) is (dy)/(dx)=(2picos(pix-y))/(1+2cos(-y+pix))