Solve 2/3*1/3x

$$\frac{ 2 }{ 3 } \times \frac{ 1 }{ 3 } x$$

Evaluate

$$\frac{2x}{9}$$

Solution Steps

Multiply \frac{2}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1}{3\times 3}x$$

Do the multiplications in the fraction \frac{2\times 1}{3\times 3}.

$$\frac{2}{9}x$$

Differentiate w.r.t. x

$$\frac{2}{9} = 0.2222222222222222$$

Steps Using Definition of a Derivative

Multiply \frac{2}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\times 1}{3\times 3}x)$$

Do the multiplications in the fraction \frac{2\times 1}{3\times 3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{9}x)$$

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

$$\frac{2}{9}x^{1-1}$$

Subtract 1 from 1.

$$\frac{2}{9}x^{0}$$

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

$$\frac{2}{9}\times 1$$

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

$$\frac{2}{9}$$