Solve y^frac{1{2}+2/3-1}

$$y ^ { \frac { 1 } { 2 } + \frac { 2 } { 3 } - 1 }$$

Evaluate

$$\sqrt[6]{y}$$

Solution Steps

Add \frac{1}{2} and \frac{2}{3} to get \frac{7}{6}.

$$y^{\frac{7}{6}-1}$$

Subtract 1 from \frac{7}{6} to get \frac{1}{6}.

$$y^{\frac{1}{6}}$$

Differentiate w.r.t. y

$$\frac{1}{6y^{\frac{5}{6}}}$$

Steps Using Definition of a Derivative

Add \frac{1}{2} and \frac{2}{3} to get \frac{7}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{\frac{7}{6}-1})$$

Subtract 1 from \frac{7}{6} to get \frac{1}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{\frac{1}{6}})$$

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

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

Subtract 1 from \frac{1}{6}.

$$\frac{1}{6}y^{-\frac{5}{6}}$$