Solve (frac{63ab^{3}}{14c^2d^5})(cd^2/15a^3b)

$$( \frac { 63 a b ^ { 3 } } { 14 c ^ { 2 } d ^ { 5 } } ) ( \frac { c d ^ { 2 } } { 15 a ^ { 3 } b } )$$

Evaluate

$$\frac{3\times \left(\frac{b}{a}\right)^{2}}{10cd^{3}}$$

Solution Steps

Cancel out 7 in both numerator and denominator.

$$\frac{9ab^{3}}{2c^{2}d^{5}}\times \frac{cd^{2}}{15a^{3}b}$$

Multiply \frac{9ab^{3}}{2c^{2}d^{5}} times \frac{cd^{2}}{15a^{3}b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9ab^{3}cd^{2}}{2c^{2}d^{5}\times 15a^{3}b}$$

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

$$\frac{3b^{2}}{2\times 5ca^{2}d^{3}}$$

Multiply 2 and 5 to get 10.

$$\frac{3b^{2}}{10ca^{2}d^{3}}$$

Differentiate w.r.t. d

$$-\frac{9\times \left(\frac{b}{a}\right)^{2}}{10cd^{4}}$$