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

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

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

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

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Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

p^{2} q^{2}

35 e^{- 0.015 \cdot 17.458}

3 2 x x

(5 \cdot 1 0^{- 11}) (8.4 \cdot 1 0^{5})

\frac{1}{12} e^{4 x} \cdot e^{- x}

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