Solve 1/3*5/3x

$$\frac { 1 } { 3 } \cdot \frac { 5 } { 3 } x$$

Evaluate

$$\frac{5x}{9}$$

Solution Steps

Multiply \frac{1}{3} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{3\times 3}x$$

Do the multiplications in the fraction \frac{1\times 5}{3\times 3}.

$$\frac{5}{9}x$$

Differentiate w.r.t. x

$$\frac{5}{9} = 0.5555555555555556$$

Steps Using Definition of a Derivative

Multiply \frac{1}{3} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1\times 5}{3\times 3}x)$$

Do the multiplications in the fraction \frac{1\times 5}{3\times 3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{9}x)$$

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

$$\frac{5}{9}x^{1-1}$$

Subtract 1 from 1.

$$\frac{5}{9}x^{0}$$

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

$$\frac{5}{9}\times 1$$

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

$$\frac{5}{9}$$