Solve x^3/y^2divx/y^2

$$\frac { x ^ { 3 } } { y ^ { 2 } } \div \frac { x } { y ^ { 2 } }$$

Evaluate

$$x^{2}$$

Solution Steps

Divide \frac{x^{3}}{y^{2}} by \frac{x}{y^{2}} by multiplying \frac{x^{3}}{y^{2}} by the reciprocal of \frac{x}{y^{2}}.

$$\frac{x^{3}y^{2}}{y^{2}x}$$

Cancel out xy^{2} in both numerator and denominator.

$$x^{2}$$

Differentiate w.r.t. x

$$2x$$

Steps Using Definition of a Derivative

Divide \frac{x^{3}}{y^{2}} by \frac{x}{y^{2}} by multiplying \frac{x^{3}}{y^{2}} by the reciprocal of \frac{x}{y^{2}}.

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

Cancel out xy^{2} in both numerator and denominator.

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

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

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

Subtract 1 from 2.

$$2x^{1}$$

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

$$2x$$