Solve 6xy/15ab^2*21a^3/18x^4y

$$\frac { 6 x y } { 15 a b ^ { 2 } } \cdot \frac { 21 a ^ { 3 } } { 18 x ^ { 4 } y }$$

Evaluate

$$\frac{7\times \left(\frac{a}{b}\right)^{2}}{15x^{3}}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{2xy}{5ab^{2}}\times \frac{21a^{3}}{18x^{4}y}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2xy}{5ab^{2}}\times \frac{7a^{3}}{6yx^{4}}$$

Multiply \frac{2xy}{5ab^{2}} times \frac{7a^{3}}{6yx^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2xy\times 7a^{3}}{5ab^{2}\times 6yx^{4}}$$

Cancel out 2axy in both numerator and denominator.

$$\frac{7a^{2}}{3\times 5b^{2}x^{3}}$$

Multiply 3 and 5 to get 15.

$$\frac{7a^{2}}{15b^{2}x^{3}}$$

Differentiate w.r.t. x

$$-\frac{7\times \left(\frac{a}{b}\right)^{2}}{5x^{4}}$$