Solve p^3/3p

$$\frac { p ^ { 3 } } { 3 p }$$

Differentiate w.r.t. p

$$\frac{2p}{3}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{1}{3}p^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{1}{3}p^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times \frac{1}{3}p^{2-1}$$

Do the arithmetic.

$$\frac{2}{3}p^{1}$$

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

$$\frac{2}{3}p$$

Evaluate

$$\frac{p^{2}}{3}$$

Solution Steps

Cancel out p in both numerator and denominator.

$$\frac{p^{2}}{3}$$