Solve 18x^5y/2xy^4

$$\frac { 18 x ^ { 5 } y } { 2 x y ^ { 4 } }$$

Evaluate

$$\frac{9x^{4}}{y^{3}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{18^{1}x^{5}y^{1}}{2^{1}x^{1}y^{4}}$$

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

$$\frac{18^{1}}{2^{1}}x^{5-1}y^{1-4}$$

Subtract 1 from 5.

$$\frac{18^{1}}{2^{1}}x^{4}y^{1-4}$$

Subtract 4 from 1.

$$\frac{18^{1}}{2^{1}}x^{4}y^{-3}$$

Divide 18 by 2.

$$9x^{4}\times \frac{1}{y^{3}}$$

Differentiate w.r.t. x

$$36\times \left(\frac{x}{y}\right)^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18y}{2y^{4}}x^{5-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{y^{3}}x^{4})$$

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}.

$$4\times \frac{9}{y^{3}}x^{4-1}$$

Do the arithmetic.

$$\frac{36}{y^{3}}x^{3}$$