Solve 36x^2y^4/9xy^2

$$\frac { 36 x ^ { 2 } y ^ { 4 } } { 9 x y ^ { 2 } }$$

Evaluate

$$4xy^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{36^{1}x^{2}y^{4}}{9^{1}x^{1}y^{2}}$$

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

$$\frac{36^{1}}{9^{1}}x^{2-1}y^{4-2}$$

Subtract 1 from 2.

$$\frac{36^{1}}{9^{1}}x^{1}y^{4-2}$$

Subtract 2 from 4.

$$\frac{36^{1}}{9^{1}}xy^{2}$$

Divide 36 by 9.

$$4xy^{2}$$

Differentiate w.r.t. x

$$4y^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{36y^{4}}{9y^{2}}x^{2-1})$$

Do the arithmetic.

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

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}.

$$4y^{2}x^{1-1}$$

Do the arithmetic.

$$4y^{2}x^{0}$$

For any term t except 0, t^{0}=1.

$$4y^{2}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$4y^{2}$$