Solve 2x^2*6x*3

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

Evaluate

$$36x^{3}$$

Solution Steps

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

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

Multiply 2 and 6 to get 12.

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

Multiply 12 and 3 to get 36.

$$36x^{3}$$

Differentiate w.r.t. x

$$108x^{2}$$

Steps Using Definition of a Derivative

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

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

Multiply 2 and 6 to get 12.

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

Multiply 12 and 3 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x^{3})$$

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

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

Multiply 3 times 36.

$$108x^{3-1}$$

Subtract 1 from 3.

$$108x^{2}$$