Solve -12m^3/3m

$$\frac { - 12 m ^ { 3 } } { 3 m }$$

Evaluate

$$-4m^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-12\right)^{1}m^{3}}{3^{1}m^{1}}$$

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

$$\frac{\left(-12\right)^{1}m^{3-1}}{3^{1}}$$

Subtract 1 from 3.

$$\frac{\left(-12\right)^{1}m^{2}}{3^{1}}$$

Divide -12 by 3.

$$-4m^{2}$$

Differentiate w.r.t. m

$$-8m$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(-\frac{12}{3}\right)m^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(-4m^{2})$$

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}.

$$2\left(-4\right)m^{2-1}$$

Do the arithmetic.

$$-8m^{1}$$

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

$$-8m$$