Solve 2x/3x^2y^-1

$$\frac { 2 x } { 3 x ^ { 2 } y ^ { - 1 } }$$

Evaluate

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

Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{2}{3\times \frac{1}{y}x}$$

Express 3\times \frac{1}{y} as a single fraction.

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

Express \frac{3}{y}x as a single fraction.

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

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

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

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y}{3}x^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y}{3}\times \frac{1}{x})$$

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}.

$$-\frac{2y}{3}x^{-1-1}$$

Do the arithmetic.

$$\left(-\frac{2y}{3}\right)x^{-2}$$