Solve 30x^4y^3/-6x^7y

$$\frac { 30 x ^ { 4 } y ^ { 3 } } { - 6 x ^ { 7 } y }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{30^{1}x^{4}y^{3}}{\left(-6\right)^{1}x^{7}y^{1}}$$

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

$$\frac{30^{1}}{\left(-6\right)^{1}}x^{4-7}y^{3-1}$$

Subtract 7 from 4.

$$\frac{30^{1}}{\left(-6\right)^{1}}x^{-3}y^{3-1}$$

Subtract 1 from 3.

$$\frac{30^{1}}{\left(-6\right)^{1}}\times \frac{1}{x^{3}}y^{2}$$

Divide 30 by -6.

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

Differentiate w.r.t. x

$$\frac{15y^{2}}{x^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{30y^{3}}{-6y}x^{4-7})$$

Do the arithmetic.

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

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}.

$$-3\left(-5y^{2}\right)x^{-3-1}$$

Do the arithmetic.

$$15y^{2}x^{-4}$$