What is (\partial)/(\partial x)(3(((4+z))/(5+x))^2) ?

The answer to (\partial)/(\partial x)(3(((4+z))/(5+x))^2) is -(6(4+z)^2)/((5+x)^3)

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(\partial)/(\partial x)(3(((4+z))/(5+x))^2)

\frac{\partial}{\partial x} (3 (\frac{( 4 + z )}{5 + x})^{2})

- \frac{6 ( 4 + z ) ^{2}}{( 5 + x ) ^{3}}

Solution steps

\frac{\partial}{\partial x} (3 (\frac{( 4 + z )}{5 + x})^{2})

Treat

z

as a constant

Take the constant out:

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

= 3 \frac{\partial}{\partial x} ((\frac{4 + z}{5 + x})^{2})

Apply the chain rule:

2 \cdot \frac{4 + z}{5 + x} \frac{\partial}{\partial x} (\frac{4 + z}{5 + x})

= 2 \cdot \frac{4 + z}{5 + x} \frac{\partial}{\partial x} (\frac{4 + z}{5 + x})

\frac{\partial}{\partial x} (\frac{4 + z}{5 + x}) = - \frac{4 + z}{( 5 + x ) ^{2}}

= 3 \cdot 2 \cdot \frac{4 + z}{5 + x} (- \frac{4 + z}{( 5 + x ) ^{2}})

Simplify

3 \cdot 2 \cdot \frac{4 + z}{5 + x} (- \frac{4 + z}{( 5 + x ) ^{2}}) : - \frac{6 ( 4 + z ) ^{2}}{( 5 + x ) ^{3}}

= - \frac{6 ( 4 + z ) ^{2}}{( 5 + x ) ^{3}}

What is (\partial)/(\partial x)(3(((4+z))/(5+x))^2) ?
The answer to (\partial)/(\partial x)(3(((4+z))/(5+x))^2) is -(6(4+z)^2)/((5+x)^3)