Solve h^3/8s^2h^2/4hsk

$$\frac { \frac { h ^ { 3 } } { 8 s ^ { 2 } h ^ { 2 } } } { 4 h s k }$$

Evaluate

$$\frac{1}{32ks^{3}}$$

Solution Steps

Express \frac{\frac{h^{3}}{8s^{2}h^{2}}}{4hsk} as a single fraction.

$$\frac{h^{3}}{8s^{2}h^{2}\times 4hsk}$$

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

$$\frac{1}{4\times 8kss^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{1}{4\times 8ks^{3}}$$

Multiply 4 and 8 to get 32.

$$\frac{1}{32ks^{3}}$$

Differentiate w.r.t. k

$$-\frac{1}{32k^{2}s^{3}}$$