Solve 9m^3ndiv(-3mn)

$$9 m ^ { 3 } n \div ( - 3 m n )$$

Evaluate

$$-3m^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{9^{1}m^{3}n^{1}}{\left(-3\right)^{1}m^{1}n^{1}}$$

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

$$\frac{9^{1}}{\left(-3\right)^{1}}m^{3-1}n^{1-1}$$

Subtract 1 from 3.

$$\frac{9^{1}}{\left(-3\right)^{1}}m^{2}n^{1-1}$$

Subtract 1 from 1.

$$\frac{9^{1}}{\left(-3\right)^{1}}m^{2}n^{0}$$

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

$$\frac{9^{1}}{\left(-3\right)^{1}}m^{2}$$

Divide 9 by -3.

$$-3m^{2}$$

Differentiate w.r.t. m

$$-6m$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{9n}{-3n}m^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(-3m^{2})$$

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}.

$$2\left(-3\right)m^{2-1}$$

Do the arithmetic.

$$-6m^{1}$$

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

$$-6m$$