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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\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})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \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}}

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)}