Solve frac{frac{kh^{4}}{d^2}}{k^4h^4/d^6}

$$\frac { \frac { k h ^ { 4 } } { d ^ { 2 } } } { \frac { k ^ { 4 } h ^ { 4 } } { d ^ { 6 } } }$$

Evaluate

$$\frac{d^{4}}{k^{3}}$$

Solution Steps

Divide \frac{kh^{4}}{d^{2}} by \frac{k^{4}h^{4}}{d^{6}} by multiplying \frac{kh^{4}}{d^{2}} by the reciprocal of \frac{k^{4}h^{4}}{d^{6}}.

$$\frac{kh^{4}d^{6}}{d^{2}k^{4}h^{4}}$$

Cancel out kd^{2}h^{4} in both numerator and denominator.

$$\frac{d^{4}}{k^{3}}$$

Differentiate w.r.t. k

$$-3\times \left(\frac{d}{k}\right)^{4}$$