Solve 2xy^3/4xy^-1

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

Evaluate

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

Solution Steps

Cancel out 2x in both numerator and denominator.

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

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

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

Differentiate w.r.t. y

$$2y^{3}$$

Steps Using Definition of a Derivative

Cancel out 2x in both numerator and denominator.

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

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

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

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

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

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

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

Subtract 1 from 4.

$$2y^{3}$$