Solve y^1/3*y^5/3/y^3

$$\frac { y ^ { 1 / 3 } \cdot y ^ { 5 / 3 } } { y ^ { 3 } }$$

Evaluate

$$\frac{1}{y}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{1}{3} and \frac{5}{3} to get 2.

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

Rewrite y^{3} as y^{2}y. Cancel out y^{2} in both numerator and denominator.

$$\frac{1}{y}$$

Differentiate w.r.t. y

$$-\frac{1}{y^{2}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{1}{3} and \frac{5}{3} to get 2.

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

Rewrite y^{3} as y^{2}y. Cancel out y^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{y})$$

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

$$-y^{-1-1}$$

Subtract 1 from -1.

$$-y^{-2}$$