Solve 4x^3y^4/3xy^3

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

Evaluate

$$\frac{4yx^{2}}{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 1 from 3.

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

Subtract 3 from 4.

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

Divide 4 by 3.

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

Differentiate w.r.t. x

$$\frac{8xy}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4y^{4}}{3y^{3}}x^{3-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\frac{8y}{3}x^{1}$$

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

$$\frac{8y}{3}x$$