Solve 2(5x)(x)

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

Evaluate

$$10x^{2}$$

Solution Steps

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

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

Multiply 2 and 5 to get 10.

$$10x^{2}$$

Differentiate w.r.t. x

$$20x$$

Steps Using Definition of a Derivative

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

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

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{2})$$

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

$$2\times 10x^{2-1}$$

Multiply 2 times 10.

$$20x^{2-1}$$

Subtract 1 from 2.

$$20x^{1}$$

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

$$20x$$