Solve 10b^5c/3c^4*c/12b^2

$$\frac { 10 b ^ { 5 } c } { 3 c ^ { 4 } } \cdot \frac { c } { 12 b ^ { 2 } }$$

Evaluate

$$\frac{5b^{3}}{18c^{2}}$$

Solution Steps

Cancel out c in both numerator and denominator.

$$\frac{10b^{5}}{3c^{3}}\times \frac{c}{12b^{2}}$$

Multiply \frac{10b^{5}}{3c^{3}} times \frac{c}{12b^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10b^{5}c}{3c^{3}\times 12b^{2}}$$

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

$$\frac{5b^{3}}{3\times 6c^{2}}$$

Multiply 3 and 6 to get 18.

$$\frac{5b^{3}}{18c^{2}}$$

Differentiate w.r.t. b

$$\frac{5\times \left(\frac{b}{c}\right)^{2}}{6}$$