Solve (25bd^2/2^2c^3)div(25ab/10b)

$$( \frac { 25 b d ^ { 2 } } { 2 ^ { 2 } c ^ { 3 } } ) \div ( \frac { 25 a b } { 10 b } )$$

Evaluate

$$\frac{5bd^{2}}{2ac^{3}}$$

Solution Steps

Divide \frac{25bd^{2}}{2^{2}c^{3}} by \frac{25ab}{10b} by multiplying \frac{25bd^{2}}{2^{2}c^{3}} by the reciprocal of \frac{25ab}{10b}.

$$\frac{25bd^{2}\times 10b}{2^{2}c^{3}\times 25ab}$$

Cancel out 25b in both numerator and denominator.

$$\frac{10bd^{2}}{2^{2}ac^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{10bd^{2}}{4ac^{3}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5bd^{2}}{2ac^{3}}$$

Differentiate w.r.t. a

$$-\frac{5\times \left(\frac{d}{a}\right)^{2}b}{2c^{3}}$$