Solve 6x^3y^2/5xy^3

$$\frac { 6 x ^ { 3 } y ^ { 2 } } { 5 x y ^ { 3 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}x^{3}y^{2}}{5^{1}x^{1}y^{3}}$$

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

$$\frac{6^{1}}{5^{1}}x^{3-1}y^{2-3}$$

Subtract 1 from 3.

$$\frac{6^{1}}{5^{1}}x^{2}y^{2-3}$$

Subtract 3 from 2.

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

Divide 6 by 5.

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

Differentiate w.r.t. x

$$\frac{12x}{5y}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y^{2}}{5y^{3}}x^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6}{5y}x^{2})$$

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}.

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

Do the arithmetic.

$$\frac{12}{5y}x^{1}$$

For any term t, t^{1}=t.

$$\frac{12}{5y}x$$