Solve 72x^5y^4/-36x^2y^2

$$\frac { 72 x ^ { 5 } y ^ { 4 } } { - 36 x ^ { 2 } y ^ { 2 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{72^{1}x^{5}y^{4}}{\left(-36\right)^{1}x^{2}y^{2}}$$

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

$$\frac{72^{1}}{\left(-36\right)^{1}}x^{5-2}y^{4-2}$$

Subtract 2 from 5.

$$\frac{72^{1}}{\left(-36\right)^{1}}x^{3}y^{4-2}$$

Subtract 2 from 4.

$$\frac{72^{1}}{\left(-36\right)^{1}}x^{3}y^{2}$$

Divide 72 by -36.

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

Differentiate w.r.t. x

$$-6\left(xy\right)^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{72y^{4}}{-36y^{2}}x^{5-2})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\left(-6y^{2}\right)x^{2}$$