Solve 1/2O1/3

$$\frac { 1 } { 2 } O \frac { 1 } { 3 }$$

Evaluate

$$\frac{O}{6}$$

Solution Steps

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

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

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

$$\frac{1}{6}O$$

Differentiate w.r.t. O

$$\frac{1}{6} = 0.16666666666666666$$

Steps Using Definition of a Derivative

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}O}(\frac{1}{6}O)$$

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

$$\frac{1}{6}O^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{6}O^{0}$$

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

$$\frac{1}{6}\times 1$$

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

$$\frac{1}{6}$$