Solve -20x^4y^3/5xy=

$$\frac { - 20 x ^ { 4 } y ^ { 3 } } { 5 x y } =$$

Evaluate

$$-4y^{2}x^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-20\right)^{1}x^{4}y^{3}}{5^{1}x^{1}y^{1}}$$

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

$$\frac{\left(-20\right)^{1}}{5^{1}}x^{4-1}y^{3-1}$$

Subtract 1 from 4.

$$\frac{\left(-20\right)^{1}}{5^{1}}x^{3}y^{3-1}$$

Subtract 1 from 3.

$$\frac{\left(-20\right)^{1}}{5^{1}}x^{3}y^{2}$$

Divide -20 by 5.

$$-4x^{3}y^{2}$$

Differentiate w.r.t. x

$$-12\left(xy\right)^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{20y^{3}}{5y}\right)x^{4-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-4y^{2}\right)x^{3})$$

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}.

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

Do the arithmetic.

$$\left(-12y^{2}\right)x^{2}$$