Solve -3m^2div6m^3

$$- 3 m ^ { 2 } \div 6 m ^ { 3 }$$

Evaluate

$$-\frac{m^{5}}{2}$$

Solution Steps

Divide -3m^{2} by 6 to get -\frac{1}{2}m^{2}.

$$-\frac{1}{2}m^{2}m^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-\frac{1}{2}m^{5}$$

Differentiate w.r.t. m

$$-\frac{5m^{4}}{2}$$

Steps Using Definition of a Derivative

Divide -3m^{2} by 6 to get -\frac{1}{2}m^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(-\frac{1}{2}m^{2}m^{3})$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}m}(-\frac{1}{2}m^{5})$$

The derivative of ax^{n} is nax^{n-1}.

$$5\left(-\frac{1}{2}\right)m^{5-1}$$

Multiply 5 times -\frac{1}{2}.

$$-\frac{5}{2}m^{5-1}$$

Subtract 1 from 5.

$$-\frac{5}{2}m^{4}$$