Solve 3xydivx/y=

$$3 x y \div \frac { x } { y } =$$

Evaluate

$$3y^{2}$$

Solution Steps

Divide 3xy by \frac{x}{y} by multiplying 3xy by the reciprocal of \frac{x}{y}.

$$\frac{3xyy}{x}$$

Cancel out x in both numerator and denominator.

$$3yy$$

Multiply y and y to get y^{2}.

$$3y^{2}$$

Differentiate w.r.t. y

$$6y$$

Steps Using Definition of a Derivative

Divide 3xy by \frac{x}{y} by multiplying 3xy by the reciprocal of \frac{x}{y}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3xyy}{x})$$

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(3yy)$$

Multiply y and y to get y^{2}.

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

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

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

Multiply 2 times 3.

$$6y^{2-1}$$

Subtract 1 from 2.

$$6y^{1}$$

For any term t, t^{1}=t.

$$6y$$