Solve 6x^5y^2/8xy^4

$$\frac { 6 x ^ { 5 } y ^ { 2 } } { 8 x y ^ { 4 } }$$

Evaluate

$$\frac{3x^{4}}{4y^{2}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}x^{5}y^{2}}{8^{1}x^{1}y^{4}}$$

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

$$\frac{6^{1}}{8^{1}}x^{5-1}y^{2-4}$$

Subtract 1 from 5.

$$\frac{6^{1}}{8^{1}}x^{4}y^{2-4}$$

Subtract 4 from 2.

$$\frac{6^{1}}{8^{1}}x^{4}y^{-2}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

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

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y^{2}}{8y^{4}}x^{5-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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