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

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

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 1 from 1.

$$3^{0}x^{1-3}y^{4-3}$$

For any number a except 0, a^{0}=1.

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

Subtract 3 from 1.

$$x^{-2}y^{4-3}$$

Subtract 3 from 4.

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

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

$$x^{-2}y$$

Differentiate w.r.t. x

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

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(yx^{-2})$$

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}.

$$-2yx^{-2-1}$$

Do the arithmetic.

$$\left(-2y\right)x^{-3}$$