What is the first derivative of a*x+b ?

The first derivative of a*x+b is a

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derivative of a*x+b

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

a

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= a + 0

Simplify

= a

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