Solve -15x^15y^7/-3x^2y^8

$$\frac { - 15 x ^ { 15 } y ^ { 7 } } { - 3 x ^ { 2 } y ^ { 8 } }$$

Evaluate

$$\frac{5x^{13}}{y}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-15\right)^{1}x^{15}y^{7}}{\left(-3\right)^{1}x^{2}y^{8}}$$

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

$$\frac{\left(-15\right)^{1}}{\left(-3\right)^{1}}x^{15-2}y^{7-8}$$

Subtract 2 from 15.

$$\frac{\left(-15\right)^{1}}{\left(-3\right)^{1}}x^{13}y^{7-8}$$

Subtract 8 from 7.

$$\frac{\left(-15\right)^{1}}{\left(-3\right)^{1}}x^{13}\times \frac{1}{y}$$

Divide -15 by -3.

$$5x^{13}\times \frac{1}{y}$$

Differentiate w.r.t. x

$$\frac{65x^{12}}{y}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{15y^{7}}{-3y^{8}}\right)x^{15-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{y}x^{13})$$

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}.

$$13\times \frac{5}{y}x^{13-1}$$

Do the arithmetic.

$$\frac{65}{y}x^{12}$$