Solve 26xy/39x^2y^2

$$\frac{ 26xy }{ 39 { x }^{ 2 } { y }^{ 2 } }$$

Evaluate

$$\frac{2}{3xy}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{26^{1}x^{1}y^{1}}{39^{1}x^{2}y^{2}}$$

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

$$\frac{26^{1}}{39^{1}}x^{1-2}y^{1-2}$$

Subtract 2 from 1.

$$\frac{26^{1}}{39^{1}}\times \frac{1}{x}y^{1-2}$$

Subtract 2 from 1.

$$\frac{26^{1}}{39^{1}}\times \frac{1}{x}\times \frac{1}{y}$$

Reduce the fraction \frac{26}{39} to lowest terms by extracting and canceling out 13.

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

Differentiate w.r.t. x

$$-\frac{2}{3yx^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{26y}{39y^{2}}x^{1-2})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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