What is implicit y=sin(3x+4y) ?

The answer to implicit y=sin(3x+4y) is (dy)/(dx)=(3cos(3x+4y))/(1-4cos(3x+4y))

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implicit y=sin(3x+4y)

implicit derivative

y = sin (3 x + 4 y)

\frac{d y}{d x} = \frac{3 cos ( 3 x + 4 y )}{1 - 4 cos ( 3 x + 4 y )}

Solution steps

y = sin (3 x + 4 y)

Treat

y

y (x)

Differentiate both sides:

\frac{d y}{d x} = cos (3 x + 4 y) (3 + 4 \frac{d y}{d x})

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{3 cos ( 3 x + 4 y )}{1 - 4 cos ( 3 x + 4 y )}

\frac{d y}{d x} = \frac{3 cos ( 3 x + 4 y )}{1 - 4 cos ( 3 x + 4 y )}

x \to 2 lim (x^{2} + 5)

5 (x^{2} + 2 x)^{3}

x e^{x^{2}} (x^{2} + 1)^{8}

\int \frac{y}{3 y + 5} d y

\int e^{- 2 x} 2 x d x

What is implicit y=sin(3x+4y) ?
The answer to implicit y=sin(3x+4y) is (dy)/(dx)=(3cos(3x+4y))/(1-4cos(3x+4y))