Solve 2p*p*3p

$$2 p \times p \times 3 p$$

Evaluate

$$6p^{3}$$

Solution Steps

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

$$2p^{2}\times 3p$$

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

$$2p^{3}\times 3$$

Multiply 2 and 3 to get 6.

$$6p^{3}$$

Differentiate w.r.t. p

$$18p^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(2p^{2}\times 3p)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(2p^{3}\times 3)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}p}(6p^{3})$$

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

$$3\times 6p^{3-1}$$

Multiply 3 times 6.

$$18p^{3-1}$$

Subtract 1 from 3.

$$18p^{2}$$