Solve y/x^2divy/2x

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

Evaluate

$$\frac{2}{x}$$

Solution Steps

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

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

Cancel out xy in both numerator and denominator.

$$\frac{2}{x}$$

Differentiate w.r.t. x

$$-\frac{2}{x^{2}}$$

Steps Using Definition of a Derivative

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

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

Cancel out xy in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{x})$$

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

$$-2x^{-1-1}$$

Subtract 1 from -1.

$$-2x^{-2}$$