Solve frac{3y^frac{1{4}}}{-2/23/2}

$$\frac { 3 y ^ { \frac { 1 } { 4 } } } { - \frac { 2 } { 2 } \frac { 3 } { 2 } }$$

Evaluate

$$-2\sqrt[4]{y}$$

Solution Steps

Divide 2 by 2 to get 1.

$$\frac{3y^{\frac{1}{4}}}{-\frac{3}{2}}$$

Divide 3y^{\frac{1}{4}} by -\frac{3}{2} by multiplying 3y^{\frac{1}{4}} by the reciprocal of -\frac{3}{2}.

$$\frac{3y^{\frac{1}{4}}\times 2}{-3}$$

Cancel out -3 and -3.

$$-y^{\frac{1}{4}}\times 2$$

Multiply -1 and 2 to get -2.

$$-2y^{\frac{1}{4}}$$

Differentiate w.r.t. y

$$-\frac{1}{2y^{\frac{3}{4}}}$$

Steps Using Definition of a Derivative

Divide 2 by 2 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3y^{\frac{1}{4}}}{-\frac{3}{2}})$$

Divide 3y^{\frac{1}{4}} by -\frac{3}{2} by multiplying 3y^{\frac{1}{4}} by the reciprocal of -\frac{3}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3y^{\frac{1}{4}}\times 2}{-3})$$

Cancel out -3 and -3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-y^{\frac{1}{4}}\times 2)$$

Multiply -1 and 2 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-2y^{\frac{1}{4}})$$

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

$$\frac{1}{4}\left(-2\right)y^{\frac{1}{4}-1}$$

Multiply \frac{1}{4} times -2.

$$-\frac{1}{2}y^{\frac{1}{4}-1}$$

Subtract 1 from \frac{1}{4}.

$$-\frac{1}{2}y^{-\frac{3}{4}}$$