Solve (5x^4y^5/2xy^4)

$$( \frac { 5 x ^ { 4 } y ^ { 5 } } { 2 x y ^ { 4 } } )$$

Evaluate

$$\frac{5yx^{3}}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 1 from 4.

$$\frac{5^{1}}{2^{1}}x^{3}y^{5-4}$$

Subtract 4 from 5.

$$\frac{5^{1}}{2^{1}}x^{3}y^{1}$$

Divide 5 by 2.

$$\frac{5}{2}x^{3}y$$

Differentiate w.r.t. x

$$\frac{15yx^{2}}{2}$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

$$3\times \frac{5y}{2}x^{3-1}$$

Do the arithmetic.

$$\frac{15y}{2}x^{2}$$