Solve (6x^2)(2x)

$$( 6 x ^ { 2 } ) ( 2 x )$$

Evaluate

$$12x^{3}$$

Solution Steps

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

$$6x^{3}\times 2$$

Multiply 6 and 2 to get 12.

$$12x^{3}$$

Differentiate w.r.t. x

$$36x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3}\times 2)$$

Multiply 6 and 2 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{3})$$

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

$$3\times 12x^{3-1}$$

Multiply 3 times 12.

$$36x^{3-1}$$

Subtract 1 from 3.

$$36x^{2}$$