Solve m^5divm^3*m^2

$$m ^ { 5 } \div m ^ { 3 } \cdot m ^ { 2 }$$

Evaluate

$$m^{4}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 5 to get 2.

$$m^{2}m^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$m^{4}$$

Differentiate w.r.t. m

$$4m^{3}$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 5 to get 2.

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

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

$$4m^{4-1}$$

Subtract 1 from 4.

$$4m^{3}$$