What is (\partial)/(\partial x)(-(sqrt(x^2+y^2))) ?

The answer to (\partial)/(\partial x)(-(sqrt(x^2+y^2))) is -x/(sqrt(x^2+y^2))

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(\partial)/(\partial x)(-(sqrt(x^2+y^2)))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= - \frac{1}{2 x ^{2} + y ^{2}} \cdot 2 x

Simplify

- \frac{1}{2 x ^{2} + y ^{2}} \cdot 2 x : - \frac{x}{x ^{2} + y ^{2}}

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

ln (x e^{- 8 x})

y = x^{4} - 2 x^{3}, y = 0

\int e^{- x} e^{x} d x

\int_{0}^{\infty} e^{- s t} t d t

\int (1 + x) x d x

What is (\partial)/(\partial x)(-(sqrt(x^2+y^2))) ?
The answer to (\partial)/(\partial x)(-(sqrt(x^2+y^2))) is -x/(sqrt(x^2+y^2))