Solve 2x/ydivx/2y^2=

$$\frac { 2 x } { y } \div \frac { x } { 2 y ^ { 2 } } =$$

Evaluate

$$4y$$

Solution Steps

Divide \frac{2x}{y} by \frac{x}{2y^{2}} by multiplying \frac{2x}{y} by the reciprocal of \frac{x}{2y^{2}}.

$$\frac{2x\times 2y^{2}}{yx}$$

Cancel out xy in both numerator and denominator.

$$2\times 2y$$

Multiply 2 and 2 to get 4.

$$4y$$

Differentiate w.r.t. y

$$4$$

Steps Using Definition of a Derivative

Divide \frac{2x}{y} by \frac{x}{2y^{2}} by multiplying \frac{2x}{y} by the reciprocal of \frac{x}{2y^{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2x\times 2y^{2}}{yx})$$

Cancel out xy in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

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

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

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

Subtract 1 from 1.

$$4y^{0}$$

For any term t except 0, t^{0}=1.

$$4\times 1$$

For any term t, t\times 1=t and 1t=t.

$$4$$