Solve 19x^10y^14/8x^7y^5

$$\frac { 19 x ^ { 10 } y ^ { 14 } } { 8 x ^ { 7 } y ^ { 5 } }$$

Evaluate

$$\frac{19x^{3}y^{9}}{8}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{19^{1}x^{10}y^{14}}{8^{1}x^{7}y^{5}}$$

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

$$\frac{19^{1}}{8^{1}}x^{10-7}y^{14-5}$$

Subtract 7 from 10.

$$\frac{19^{1}}{8^{1}}x^{3}y^{14-5}$$

Subtract 5 from 14.

$$\frac{19^{1}}{8^{1}}x^{3}y^{9}$$

Divide 19 by 8.

$$\frac{19}{8}x^{3}y^{9}$$

Differentiate w.r.t. x

$$\frac{57x^{2}y^{9}}{8}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{19y^{14}}{8y^{5}}x^{10-7})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{19y^{9}}{8}x^{3})$$

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}.

$$3\times \frac{19y^{9}}{8}x^{3-1}$$

Do the arithmetic.

$$\frac{57y^{9}}{8}x^{2}$$