Solve 6x*3x*2x=

$$6 x \cdot 3 x \cdot 2 x =$$

Evaluate

$$36x^{3}$$

Solution Steps

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

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

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

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

Multiply 6 and 3 to get 18.

$$18x^{3}\times 2$$

Multiply 18 and 2 to get 36.

$$36x^{3}$$

Differentiate w.r.t. x

$$108x^{2}$$

Steps Using Definition of a Derivative

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

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

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

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

Multiply 6 and 3 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{3}\times 2)$$

Multiply 18 and 2 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.

$$108x^{2}$$