Solve -14r^{3}s^{11}+15r^-1s^15/5r^-4s^4

$$- 14 r ^ { 3 } s ^ { 11 } + \frac { 15 r ^ { - 1 } s ^ { 15 } } { 5 r ^ { - 4 } s ^ { 4 } }$$

Evaluate

$$-11r^{3}s^{11}$$

Solution Steps

Cancel out 5s^{4} in both numerator and denominator.

$$-14r^{3}s^{11}+\frac{3\times \frac{1}{r}s^{11}}{r^{-4}}$$

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

$$-14r^{3}s^{11}+3r^{3}s^{11}$$

Combine -14r^{3}s^{11} and 3r^{3}s^{11} to get -11r^{3}s^{11}.

$$-11r^{3}s^{11}$$

Differentiate w.r.t. r

$$-33r^{2}s^{11}$$