Solve 20m^-3n^4/4m^8n^6

$$\frac { 20 m ^ { - 3 } n ^ { 4 } } { 4 m ^ { 8 } n ^ { 6 } }$$

Evaluate

$$\frac{5}{n^{2}m^{11}}$$

Solution Steps

Cancel out 4n^{4} in both numerator and denominator.

$$\frac{5m^{-3}}{n^{2}m^{8}}$$

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

$$\frac{5}{n^{2}m^{11}}$$

Differentiate w.r.t. m

$$-\frac{55}{n^{2}m^{12}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{20n^{4}}{4n^{6}}m^{-3-8})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{5}{n^{2}}m^{-11})$$

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}.

$$-11\times \frac{5}{n^{2}}m^{-11-1}$$

Do the arithmetic.

$$\left(-\frac{55}{n^{2}}\right)m^{-12}$$