What is the d/(dp)(prt) ?

The d/(dp)(prt) is t(r(p,t)+p d/(dp)(r(p,t)))

What is the first d/(dp)(prt) ?

The first d/(dp)(prt) is t(r(p,t)+p d/(dp)(r(p,t)))

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\frac{d}{d p} (p r (p, t) t)

t (r (p, t) + p \frac{d}{d p} (r (p, t)))

Solution steps

\frac{d}{d p} (p r (p, t) t)

Treat

t

as a constant

Take the constant out:

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

= t \frac{d}{d p} (p r (p, t))

Apply the Product Rule:

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

f = p, g = r (p, t)

= t (\frac{d p}{d p} r (p, t) + \frac{d}{d p} (r (p, t)) p)

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

= t (1 \cdot r (p, t) + \frac{d}{d p} (r (p, t)) p)

Simplify

= t (r (p, t) + p \frac{d}{d p} (r (p, t)))

\frac{2 - 10}{2 + 10}

4^{2} - 5 x - 6

3 + (- 1)

\frac{1}{6} \cdot 27

6 x^{2} - 5 x - 25

What is the d/(dp)(prt) ?
The d/(dp)(prt) is t(r(p,t)+p d/(dp)(r(p,t)))
What is the first d/(dp)(prt) ?
The first d/(dp)(prt) is t(r(p,t)+p d/(dp)(r(p,t)))