Solve PePP

$$P e P P$$

Evaluate

$$eP^{3}$$

Solution Steps

Multiply P and P to get P^{2}.

$$P^{2}eP$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$P^{3}e$$

Differentiate w.r.t. P

$$3eP^{2}$$

Steps Using Definition of a Derivative

Multiply P and P to get P^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}P}(P^{2}eP)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}P}(P^{3}e)$$

The derivative of ax^{n} is nax^{n-1}.

$$3eP^{3-1}$$

Subtract 1 from 3.

$$3eP^{2}$$