Solve x*4x*6x=

$$x \times 4x \times 6x=$$

Evaluate

$$24x^{3}$$

Solution Steps

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

$$x^{2}\times 4\times 6x$$

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

$$x^{3}\times 4\times 6$$

Multiply 4 and 6 to get 24.

$$x^{3}\times 24$$

Differentiate w.r.t. x

$$72x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\times 4\times 6x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\times 4\times 6)$$

Multiply 4 and 6 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\times 24)$$

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

$$3\times 24x^{3-1}$$

Multiply 3 times 24.

$$72x^{3-1}$$

Subtract 1 from 3.

$$72x^{2}$$