Solve (3p)(5p)(2p)

$$( 3 p ) ( 5 p ) ( 2 p )$$

Evaluate

$$30p^{3}$$

Solution Steps

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

$$3p^{2}\times 5\times 2p$$

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

$$3p^{3}\times 5\times 2$$

Multiply 3 and 5 to get 15.

$$15p^{3}\times 2$$

Multiply 15 and 2 to get 30.

$$30p^{3}$$

Differentiate w.r.t. p

$$90p^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(3p^{2}\times 5\times 2p)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(3p^{3}\times 5\times 2)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}p}(15p^{3}\times 2)$$

Multiply 15 and 2 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}p}(30p^{3})$$

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

$$3\times 30p^{3-1}$$

Multiply 3 times 30.

$$90p^{3-1}$$

Subtract 1 from 3.

$$90p^{2}$$