Solve 0.1x*0.1x

$$0.1x \times 0.1x$$

Evaluate

$$\frac{x^{2}}{100}$$

Solution Steps

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

$$0.1x^{2}\times 0.1$$

Multiply 0.1 and 0.1 to get 0.01.

$$0.01x^{2}$$

Differentiate w.r.t. x

$$\frac{x}{50}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(0.1x^{2}\times 0.1)$$

Multiply 0.1 and 0.1 to get 0.01.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0.01x^{2})$$

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

$$2\times 0.01x^{2-1}$$

Multiply 2 times 0.01.

$$0.02x^{2-1}$$

Subtract 1 from 2.

$$0.02x^{1}$$

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

$$0.02x$$