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{d}{d z} (x e^{z})

\int (x^{2} + 2 x - 10)^{\frac{2}{3}} (5 x + 5) d x

l a pl a ce t r an s f or m e^{- 2 t} - 3 cos (2 t)

\frac{d}{d x} (- 2 cos (x))

\frac{d}{d x} (1 + tan (x))

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)