What is (\partial)/(\partial x)(3/(x^2+z^2)) ?

The answer to (\partial)/(\partial x)(3/(x^2+z^2)) is -(6x)/((x^2+z^2)^2)

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(\partial)/(\partial x)(3/(x^2+z^2))

\frac{\partial}{\partial x} (\frac{3}{x ^{2} + z ^{2}})

- \frac{6 x}{( x ^{2} + z ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{3}{x ^{2} + z ^{2}})

Treat

z

as a constant

Take the constant out:

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

= 3 \frac{\partial}{\partial x} (\frac{1}{x ^{2} + z ^{2}})

Apply exponent rule:

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

= 3 \frac{\partial}{\partial x} ((x^{2} + z^{2})^{- 1})

Apply the chain rule:

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

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

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

= 3 (- \frac{1}{( x ^{2} + z ^{2} ) ^{2}} \cdot 2 x)

Simplify

3 (- \frac{1}{( x ^{2} + z ^{2} ) ^{2}} \cdot 2 x) : - \frac{6 x}{( x ^{2} + z ^{2} ) ^{2}}

= - \frac{6 x}{( x ^{2} + z ^{2} ) ^{2}}

\frac{\partial}{\partial x} (x^{3} y - y^{3})

d (x) \frac{55}{0.01 x ^{2} + 1}

\int_{1}^{2} \frac{1}{x ^{6}} d x

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

\frac{d}{d x} ((6 x)^{- 5})

What is (\partial)/(\partial x)(3/(x^2+z^2)) ?
The answer to (\partial)/(\partial x)(3/(x^2+z^2)) is -(6x)/((x^2+z^2)^2)