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Popular Calculus >

derivative of xy=c^2

Solution

derivative of

x y = c^{2}

Solution

\frac{d y}{d x} = - \frac{y}{x}

Solution steps

x y = c^{2}

Treat

y

as

y (x)

Differentiate both sides:

y + x \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y}{x}

\frac{d y}{d x} = - \frac{y}{x}

Popular Examples

derivative of x^y=x^3+2sin(x)

d er i v a t i v e x^{y} = x^{3} + 2 sin (x)

derivative of 1-x^3=t^2

d er i v a t i v e 1 - x^{3} = t^{2}

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

d er i v a t i v e x^{2} - y^{2} = tan (x) y

derivative of x=(y+1)/y

d er i v a t i v e x = \frac{y + 1}{y}

derivative of 2x^3+4x^2-y=x^6

d er i v a t i v e 2 x^{3} + 4 x^{2} - y = x^{6}

Frequently Asked Questions (FAQ)

What is derivative of xy=c^2 ?
The answer to derivative of xy=c^2 is (dy)/(dx)=-y/x