Solve 26x^12y^18/34x^5y^8

$$\frac { 26 x ^ { 12 } y ^ { 18 } } { 34 x ^ { 5 } y ^ { 8 } }$$

Evaluate

$$\frac{13x^{7}y^{10}}{17}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{26^{1}x^{12}y^{18}}{34^{1}x^{5}y^{8}}$$

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

$$\frac{26^{1}}{34^{1}}x^{12-5}y^{18-8}$$

Subtract 5 from 12.

$$\frac{26^{1}}{34^{1}}x^{7}y^{18-8}$$

Subtract 8 from 18.

$$\frac{26^{1}}{34^{1}}x^{7}y^{10}$$

Reduce the fraction \frac{26}{34} to lowest terms by extracting and canceling out 2.

$$\frac{13}{17}x^{7}y^{10}$$

Differentiate w.r.t. x

$$\frac{91x^{6}y^{10}}{17}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{26y^{18}}{34y^{8}}x^{12-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{13y^{10}}{17}x^{7})$$

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}.

$$7\times \frac{13y^{10}}{17}x^{7-1}$$

Do the arithmetic.

$$\frac{91y^{10}}{17}x^{6}$$