What is the derivative of 1/((x^2+y^2)) ?

The derivative of 1/((x^2+y^2)) is -(2x)/((x^2+y^2)^2)

What is the first derivative of 1/((x^2+y^2)) ?

The first derivative of 1/((x^2+y^2)) is -(2x)/((x^2+y^2)^2)

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derivative of

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

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

Solution steps

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

Treat

y

as a constant

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(\frac{x + 1}{x})^{3}

\frac{d}{d x} ((x - h)^{2} + k)

f (x) = \frac{1}{( 2 x ^{2} )}

e^{- 5} x

f (x) = - 2 x^{2} - 5

What is the derivative of 1/((x^2+y^2)) ?
The derivative of 1/((x^2+y^2)) is -(2x)/((x^2+y^2)^2)
What is the first derivative of 1/((x^2+y^2)) ?
The first derivative of 1/((x^2+y^2)) is -(2x)/((x^2+y^2)^2)