Solve 2x*3x^2

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

Evaluate

$$6x^{3}$$

Solution Steps

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

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

Multiply 2 and 3 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.

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

Multiply 2 and 3 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.

$$18x^{2}$$