Solve 2x*2x*3x

$$2 x \times 2 x \times 3 x$$

Evaluate

$$12x^{3}$$

Solution Steps

Multiply x and x to get x^{2}.

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

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

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

Multiply 2 and 2 to get 4.

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

Multiply 4 and 3 to get 12.

$$12x^{3}$$

Differentiate w.r.t. x

$$36x^{2}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

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

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

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

Multiply 2 and 2 to get 4.

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

Multiply 4 and 3 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.

$$36x^{2}$$