What is derivative of x^y=y^2 ?

The answer to derivative of x^y=y^2 is (dy)/(dx)=-(yx^{y-1})/(x^yln(x)-2y)

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derivative of x^y=y^2

derivative of

x^{y} = y^{2}

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

Solution steps

x^{y} = y^{2}

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

y^{2} = - 4 x + 3

x^{5} + y^{4} = 500

s = \frac{1}{t}

x^{2} + y^{2} x + 6 x = 1

x = \frac{y ^{3}}{3 + y}

What is derivative of x^y=y^2 ?
The answer to derivative of x^y=y^2 is (dy)/(dx)=-(yx^{y-1})/(x^yln(x)-2y)