Solve -63x^13y^7/7x^5y^2

$$\frac { - 63 x ^ { 13 } y ^ { 7 } } { 7 x ^ { 5 } y ^ { 2 } }$$

Evaluate

$$-9y^{5}x^{8}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-63\right)^{1}x^{13}y^{7}}{7^{1}x^{5}y^{2}}$$

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

$$\frac{\left(-63\right)^{1}}{7^{1}}x^{13-5}y^{7-2}$$

Subtract 5 from 13.

$$\frac{\left(-63\right)^{1}}{7^{1}}x^{8}y^{7-2}$$

Subtract 2 from 7.

$$\frac{\left(-63\right)^{1}}{7^{1}}x^{8}y^{5}$$

Divide -63 by 7.

$$-9x^{8}y^{5}$$

Differentiate w.r.t. x

$$-72y^{5}x^{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{63y^{7}}{7y^{2}}\right)x^{13-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-9y^{5}\right)x^{8})$$

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}.

$$8\left(-9y^{5}\right)x^{8-1}$$

Do the arithmetic.

$$\left(-72y^{5}\right)x^{7}$$