What is the derivative of (ax+b/c) ?

The derivative of (ax+b/c) is a/c

What is the first derivative of (ax+b/c) ?

The first derivative of (ax+b/c) is a/c

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

\frac{a}{c}

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (a x) = a

\frac{d b}{d x} = 0

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

Simplify

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

= \frac{a}{c}

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What is the derivative of (ax+b/c) ?
The derivative of (ax+b/c) is a/c
What is the first derivative of (ax+b/c) ?
The first derivative of (ax+b/c) is a/c