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

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

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

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

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

Solution steps

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

Treat

z

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (\frac{4 + x}{5 + z}) = \frac{1}{5 + z}

= 3 \cdot 2 \cdot \frac{4 + x}{5 + z} \cdot \frac{1}{5 + z}

Simplify

3 \cdot 2 \cdot \frac{4 + x}{5 + z} \cdot \frac{1}{5 + z} : \frac{6 ( 4 + x )}{( 5 + z ) ^{2}}

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

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\frac{\partial}{\partial x} (\frac{1}{e ^{x} - 1})

f (x) = e^{x} \cdot x

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