Solve 3p_{2}*2!

$$3 p _ { 2 } \times 2 !$$

Evaluate

$$6p_{2}$$

Solution Steps

The factorial of 2 is 2.

$$3p_{2}\times 2$$

Multiply 3 and 2 to get 6.

$$6p_{2}$$

Differentiate w.r.t. p_2

$$6$$

Steps Using Definition of a Derivative

The factorial of 2 is 2.

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

Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}p_{2}}(6p_{2})$$

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

$$6p_{2}^{1-1}$$

Subtract 1 from 1.

$$6p_{2}^{0}$$

For any term t except 0, t^{0}=1.

$$6\times 1$$

For any term t, t\times 1=t and 1t=t.

$$6$$