Solve (3x)(+2x^2)

$$(3x)(+2 { x }^{ 2 } )$$

Evaluate

$$6x^{3}$$

Solution Steps

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

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

Multiply 3 and 2 to get 6.

$$6x^{3}$$

Differentiate w.r.t. x

$$18x^{2}$$

Steps Using Definition of a Derivative

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

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

Multiply 3 and 2 to get 6.

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

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

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

Multiply 3 times 6.

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

Subtract 1 from 3.

$$18x^{2}$$