What is the first derivative of a+bx ?

The first derivative of a+bx is b

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derivative of a+bx

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

b

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + b

Simplify

= b

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