Solve -9x^8y^7/3x^3y^5

$$\frac { - 9 x ^ { 8 } y ^ { 7 } } { 3 x ^ { 3 } y ^ { 5 } }$$

Evaluate

$$-3y^{2}x^{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-9\right)^{1}x^{8}y^{7}}{3^{1}x^{3}y^{5}}$$

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

$$\frac{\left(-9\right)^{1}}{3^{1}}x^{8-3}y^{7-5}$$

Subtract 3 from 8.

$$\frac{\left(-9\right)^{1}}{3^{1}}x^{5}y^{7-5}$$

Subtract 5 from 7.

$$\frac{\left(-9\right)^{1}}{3^{1}}x^{5}y^{2}$$

Divide -9 by 3.

$$-3x^{5}y^{2}$$

Differentiate w.r.t. x

$$-15y^{2}x^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{9y^{7}}{3y^{5}}\right)x^{8-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-3y^{2}\right)x^{5})$$

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}.

$$5\left(-3y^{2}\right)x^{5-1}$$

Do the arithmetic.

$$\left(-15y^{2}\right)x^{4}$$