Solve 24y^3b^3div(-2yb)

$$24 y ^ { 3 } b ^ { 3 } \div ( - 2 y b )$$

Evaluate

$$-12\left(by\right)^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{24^{1}y^{3}b^{3}}{\left(-2\right)^{1}y^{1}b^{1}}$$

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

$$\frac{24^{1}}{\left(-2\right)^{1}}y^{3-1}b^{3-1}$$

Subtract 1 from 3.

$$\frac{24^{1}}{\left(-2\right)^{1}}y^{2}b^{3-1}$$

Subtract 1 from 3.

$$\frac{24^{1}}{\left(-2\right)^{1}}y^{2}b^{2}$$

Divide 24 by -2.

$$-12y^{2}b^{2}$$

Differentiate w.r.t. y

$$-24yb^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{24b^{3}}{-2b}y^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(-12b^{2}\right)y^{2})$$

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}.

$$2\left(-12b^{2}\right)y^{2-1}$$

Do the arithmetic.

$$\left(-24b^{2}\right)y^{1}$$

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

$$\left(-24b^{2}\right)y$$