What is derivative of 3+sin(y)=y-x^3 ?

The answer to derivative of 3+sin(y)=y-x^3 is (dy)/(dx)=-(3x^2)/(cos(y)-1)

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derivative of 3+sin(y)=y-x^3

derivative of

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

\frac{d y}{d x} = - \frac{3 x ^{2}}{cos ( y ) - 1}

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

cos (y) \frac{d y}{d x} = \frac{d y}{d x} - 3 x^{2}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{3 x ^{2}}{cos ( y ) - 1}

\frac{d y}{d x} = - \frac{3 x ^{2}}{cos ( y ) - 1}

x^{2} + 2 x y = 3 y^{2}

x^{2} + y^{2} = 9

2 x y - 4 y + 5 = 0

x = cos^{4} (t)

x^{4} + y^{4} = 4 a^{2} x^{3} y^{3}

What is derivative of 3+sin(y)=y-x^3 ?
The answer to derivative of 3+sin(y)=y-x^3 is (dy)/(dx)=-(3x^2)/(cos(y)-1)