Solve x^2/xy

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

Differentiate w.r.t. x

$$\frac{1}{y}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{y}x^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{y}x^{1})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{y}x^{1-1}$$

Do the arithmetic.

$$\frac{1}{y}x^{0}$$

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

$$\frac{1}{y}\times 1$$

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

$$\frac{1}{y}$$

Evaluate

$$\frac{x}{y}$$

Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{x}{y}$$