Solve (6)(2x)(5x)

$$( 6 ) ( 2 x ) ( 5 x )$$

Evaluate

$$60x^{2}$$

Solution Steps

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

$$6\times 2x^{2}\times 5$$

Multiply 6 and 2 to get 12.

$$12x^{2}\times 5$$

Multiply 12 and 5 to get 60.

$$60x^{2}$$

Differentiate w.r.t. x

$$120x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(6\times 2x^{2}\times 5)$$

Multiply 6 and 2 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{2}\times 5)$$

Multiply 12 and 5 to get 60.

$$\frac{\mathrm{d}}{\mathrm{d}x}(60x^{2})$$

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

$$2\times 60x^{2-1}$$

Multiply 2 times 60.

$$120x^{2-1}$$

Subtract 1 from 2.

$$120x^{1}$$

For any term t, t^{1}=t.

$$120x$$