Solve frac{y^frac{2{5}}(y^3)^frac{1{2}}}{y^frac{1{10}}}

$$\frac { y ^ { \frac { 2 } { 5 } } ( y ^ { 3 } ) ^ { \frac { 1 } { 2 } } } { y ^ { \frac { 1 } { 10 } } }$$

Differentiate w.r.t. y

$$\frac{9y^{\frac{4}{5}}}{5}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{\frac{2}{5}}y^{\frac{3}{2}}}{y^{\frac{1}{10}}})$$

To multiply powers of the same base, add their exponents. Add \frac{2}{5} and \frac{3}{2} to get \frac{19}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{\frac{19}{10}}}{y^{\frac{1}{10}}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract \frac{1}{10} from \frac{19}{10} to get \frac{9}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{\frac{9}{5}})$$

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

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

Subtract 1 from \frac{9}{5}.

$$\frac{9}{5}y^{\frac{4}{5}}$$

Evaluate

$$y^{\frac{9}{5}}$$