What is the first derivative of px+d ?

The first derivative of px+d is x

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derivative of px+d

derivative of

p x + d

x

Solution steps

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

Treat

d, x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{dd}{d p} = 0

= x + 0

Simplify

= x

\frac{d}{d x} (4 x ln (x) + 10)

\frac{d}{d x} (4 x^{2} - x + x)

e^{x} + \frac{1}{1 + x}

\frac{d}{d t} (ln (sec (t)))

\frac{d ^{2}}{d x ^{2}} (x^{2} cos (x))