Solve 33m^3n^4p/-9m^4n^5p

$$\frac { 33 m ^ { 3 } n ^ { 4 } p } { - 9 m ^ { 4 } n ^ { 5 } p }$$

Differentiate w.r.t. m

$$\frac{11}{3nm^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{33pn^{4}}{-9pn^{5}}m^{3-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(-\frac{11}{3n}\right)\times \frac{1}{m})$$

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}.

$$-\left(-\frac{11}{3n}\right)m^{-1-1}$$

Do the arithmetic.

$$\frac{11}{3n}m^{-2}$$

Evaluate

$$-\frac{11}{3mn}$$

Solution Steps

Cancel out 3pm^{3}n^{4} in both numerator and denominator.

$$\frac{11}{-3mn}$$