What is (\partial)/(\partial x)(((a+cx))/(c+b)) ?

The answer to (\partial)/(\partial x)(((a+cx))/(c+b)) is c/(c+b)

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(\partial)/(\partial x)(((a+cx))/(c+b))

\frac{\partial}{\partial x} (\frac{( a + c x )}{c + b})

\frac{c}{c + b}

Solution steps

\frac{\partial}{\partial x} (\frac{( a + c x )}{c + b})

Take the constant out:

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

= \frac{1}{c + b} \frac{\partial}{\partial x} (a + c x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{c + b} (\frac{\partial}{\partial x} (a) + \frac{\partial}{\partial x} (c x))

\frac{\partial}{\partial x} (a) = 0

\frac{\partial}{\partial x} (c x) = c

= \frac{1}{c + b} (0 + c)

Simplify

\frac{1}{c + b} (0 + c) : \frac{c}{c + b}

= \frac{c}{c + b}

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What is (\partial)/(\partial x)(((a+cx))/(c+b)) ?
The answer to (\partial)/(\partial x)(((a+cx))/(c+b)) is c/(c+b)