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Popular >

derivative of 1-sqrt(x^2+y^2)

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (1) = 0

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

= 0 - \frac{x + y \frac{d y}{d x}}{x ^{2} + y ^{2}}

Simplify

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

Popular Examples

integral of (x+1)/(3x+2)

\int \frac{x + 1}{3 x + 2} d x

integral from-3 to 1 of x

\int_{- 3}^{1} x d x

limit as x approaches infinity of 2ln(x)

x \to \infty lim (2 ln (x))

limit as x approaches-6 of 5x^2+6x+a

x \to - 6 lim (5 x^{2} + 6 x + a)

integral from 0 to e of 1/(x+e)

\int_{0}^{e} \frac{1}{x + e} d x

Frequently Asked Questions (FAQ)

What is the derivative of 1-sqrt(x^2+y^2) ?
The derivative of 1-sqrt(x^2+y^2) is -(x+y\frac{dy)/(dx)}{sqrt(x^2+y^2)}
What is the first derivative of 1-sqrt(x^2+y^2) ?
The first derivative of 1-sqrt(x^2+y^2) is -(x+y\frac{dy)/(dx)}{sqrt(x^2+y^2)}