What is derivative of x^2-y^2=tan(x)y ?

The answer to derivative of x^2-y^2=tan(x)y is (dy)/(dx)=-(ysec^2(x)-2x)/(tan(x)+2y)

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derivative of x^2-y^2=tan(x)y

derivative of

x^{2} - y^{2} = tan (x) y

\frac{d y}{d x} = - \frac{y sec ^{2} ( x ) - 2 x}{tan ( x ) + 2 y}

Solution steps

x^{2} - y^{2} = tan (x) y

Treat

y

y (x)

Differentiate both sides:

2 x - 2 y \frac{d y}{d x} = sec^{2} (x) y + \frac{d y}{d x} tan (x)

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y sec ^{2} ( x ) - 2 x}{tan ( x ) + 2 y}

\frac{d y}{d x} = - \frac{y sec ^{2} ( x ) - 2 x}{tan ( x ) + 2 y}

x = \frac{y + 1}{y}

2 x^{3} + 4 x^{2} - y = x^{6}

y + 5 i = (2 x + i) (x + 2 i)

x = 70 y - y^{2}

2 y^{3} x + x^{3} = y^{5} + 12

What is derivative of x^2-y^2=tan(x)y ?
The answer to derivative of x^2-y^2=tan(x)y is (dy)/(dx)=-(ysec^2(x)-2x)/(tan(x)+2y)