What is (\partial)/(\partial x)((86)/(2+x^2+y^2)) ?

The answer to (\partial)/(\partial x)((86)/(2+x^2+y^2)) is -(172x)/((2+x^2+y^2)^2)

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(\partial)/(\partial x)((86)/(2+x^2+y^2))

\frac{\partial}{\partial x} (\frac{86}{2 + x ^{2} + y ^{2}})

- \frac{172 x}{( 2 + x ^{2} + y ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{86}{2 + x ^{2} + y ^{2}})

Treat

y

as a constant

Take the constant out:

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

= 86 \frac{\partial}{\partial x} (\frac{1}{2 + x ^{2} + y ^{2}})

Apply exponent rule:

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

= 86 \frac{\partial}{\partial x} ((2 + x^{2} + y^{2})^{- 1})

Apply the chain rule:

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

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

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

= 86 (- \frac{1}{( 2 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

Simplify

86 (- \frac{1}{( 2 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{172 x}{( 2 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{172 x}{( 2 + x ^{2} + y ^{2} ) ^{2}}

\frac{d}{d x} ((2 x - 2)^{4} (x^{2} + x + 1)^{5})

\int sin (2 x) cos (4 x) d x

\int_{1}^{3} 4 x e^{x} d x

x \to 1 lim (π)

sin (π x)

What is (\partial)/(\partial x)((86)/(2+x^2+y^2)) ?
The answer to (\partial)/(\partial x)((86)/(2+x^2+y^2)) is -(172x)/((2+x^2+y^2)^2)