Solve x/3*1/3

$$\frac { x } { 3 } \times \frac { 1 } { 3 }$$

Evaluate

$$\frac{x}{9}$$

Solution Steps

Multiply \frac{x}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{x}{9}$$

Differentiate w.r.t. x

$$\frac{1}{9} = 0.1111111111111111$$

Steps Using Definition of a Derivative

Multiply \frac{x}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{9})$$

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

$$\frac{1}{9}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{9}x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1}{9}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{9}$$