Solve m^9divm^4*m^3

$$m ^ { 9 } \div m ^ { 4 } \cdot m ^ { 3 }$$

Evaluate

$$m^{8}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 9 to get 5.

$$m^{5}m^{3}$$

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$m^{8}$$

Differentiate w.r.t. m

$$8m^{7}$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 9 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{5}m^{3})$$

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{8})$$

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

$$8m^{8-1}$$

Subtract 1 from 8.

$$8m^{7}$$