Solve frac{75t^{3}}{15u^{3}v^2}*5u^3v/28s^3t^2

$$\frac { 75 t ^ { 3 } } { 15 u ^ { 3 } v ^ { 2 } } \times \frac { 5 u ^ { 3 } v } { 28 s ^ { 3 } t ^ { 2 } }$$

Evaluate

$$\frac{25t}{28vs^{3}}$$

Solution Steps

Cancel out 15 in both numerator and denominator.

$$\frac{5t^{3}}{v^{2}u^{3}}\times \frac{5u^{3}v}{28s^{3}t^{2}}$$

Multiply \frac{5t^{3}}{v^{2}u^{3}} times \frac{5u^{3}v}{28s^{3}t^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5t^{3}\times 5u^{3}v}{v^{2}u^{3}\times 28s^{3}t^{2}}$$

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

$$\frac{5\times 5t}{28vs^{3}}$$

Multiply 5 and 5 to get 25.

$$\frac{25t}{28vs^{3}}$$

Differentiate w.r.t. s

$$-\frac{75t}{28vs^{4}}$$