Solve p*4p^2

$$p \times 4 { p }^{ 2 }$$

Differentiate w.r.t. p

$$12p^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(p^{3}\times 4)$$

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

$$3\times 4p^{3-1}$$

Multiply 3 times 4.

$$12p^{3-1}$$

Subtract 1 from 3.

$$12p^{2}$$

Evaluate

$$4p^{3}$$

Solution Steps

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

$$p^{3}\times 4$$