What is the d/(dp)(3p(1-0.5p)) ?

The d/(dp)(3p(1-0.5p)) is 3(1-p)

What is the first d/(dp)(3p(1-0.5p)) ?

The first d/(dp)(3p(1-0.5p)) is 3(1-p)

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\frac{d}{d p} (3 p (1 - 0.5 p))

3 (1 - p)

Solution steps

\frac{d}{d p} (3 p (1 - 0.5 p))

Take the constant out:

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

= 3 \frac{d}{d p} (p (1 - 0.5 p))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = p, g = 1 - 0.5 p

= 3 (\frac{d p}{d p} (1 - 0.5 p) + \frac{d}{d p} (1 - 0.5 p) p)

\frac{d p}{d p} = 1

\frac{d}{d p} (1 - 0.5 p) = - 0.5

= 3 (1 \cdot (1 - 0.5 p) + (- 0.5) p)

Simplify

= 3 (1 - p)

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