Solve m^30div(m^6*m^5*m)

$$m ^ { 30 } \div ( m ^ { 6 } \times m ^ { 5 } \times m )$$

Evaluate

$$m^{18}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$\frac{m^{30}}{m^{11}m}$$

To multiply powers of the same base, add their exponents. Add 11 and 1 to get 12.

$$\frac{m^{30}}{m^{12}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 30 to get 18.

$$m^{18}$$

Differentiate w.r.t. m

$$18m^{17}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1}{mm^{5}}m^{30-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1}{m^{6}}m^{24})$$

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}.

$$24\times \frac{1}{m^{6}}m^{24-1}$$

Do the arithmetic.

$$\frac{24}{m^{6}}m^{23}$$