What is the derivative of px+b ?

The derivative of px+b is x(dp)/(dx)+p

What is the first derivative of px+b ?

The first derivative of px+b is x(dp)/(dx)+p

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

x \frac{d p}{d x} + p

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (p x) = x \frac{d p}{d x} + p

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

= x \frac{d p}{d x} + p + 0

Simplify

= x \frac{d p}{d x} + p

What is the derivative of px+b ?
The derivative of px+b is x(dp)/(dx)+p
What is the first derivative of px+b ?
The first derivative of px+b is x(dp)/(dx)+p