What is the derivative of sqrt(y^2-x^2) ?

The derivative of sqrt(y^2-x^2) is (y\frac{dy)/(dx)-x}{sqrt(y^2-x^2)}

What is the first derivative of sqrt(y^2-x^2) ?

The first derivative of sqrt(y^2-x^2) is (y\frac{dy)/(dx)-x}{sqrt(y^2-x^2)}

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Popular >

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

\frac{y \frac{d y}{d x} - x}{y ^{2} - x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{y \frac{d y}{d x} - x}{y ^{2} - x ^{2}}

\int e^{5 x + e^{5 x}} d x

\frac{s}{2 s ^{2} + 4 s + 3}

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

\int x^{3} - 2 x^{- 2} + 6 x d x

9 + x^{2}

What is the derivative of sqrt(y^2-x^2) ?
The derivative of sqrt(y^2-x^2) is (y\frac{dy)/(dx)-x}{sqrt(y^2-x^2)}
What is the first derivative of sqrt(y^2-x^2) ?
The first derivative of sqrt(y^2-x^2) is (y\frac{dy)/(dx)-x}{sqrt(y^2-x^2)}