Solve 9/r^4s^2div6/rs^6

$$\frac { 9 } { r ^ { 4 } s ^ { 2 } } \div \frac { 6 } { r s ^ { 6 } }$$

Evaluate

$$\frac{3s^{4}}{2r^{3}}$$

Solution Steps

Divide \frac{9}{r^{4}s^{2}} by \frac{6}{rs^{6}} by multiplying \frac{9}{r^{4}s^{2}} by the reciprocal of \frac{6}{rs^{6}}.

$$\frac{9rs^{6}}{r^{4}s^{2}\times 6}$$

Cancel out 3rs^{2} in both numerator and denominator.

$$\frac{3s^{4}}{2r^{3}}$$

Differentiate w.r.t. s

$$6\times \left(\frac{s}{r}\right)^{3}$$