What is derivative of y+sin(y)=x^2 ?

The answer to derivative of y+sin(y)=x^2 is (dy)/(dx)=(2x)/(1+cos(y))

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derivative of y+sin(y)=x^2

derivative of

y + sin (y) = x^{2}

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

Solution steps

y + sin (y) = x^{2}

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

x^{2} - y^{2} = 2

x = tan^{2} (y)

y^{2} = 40 x

x y = c^{2}

x^{y} = x^{3} + 2 sin (x)

What is derivative of y+sin(y)=x^2 ?
The answer to derivative of y+sin(y)=x^2 is (dy)/(dx)=(2x)/(1+cos(y))