Solve frac{3ac^{3}f^{3}}{8a^{2}bcf^4}*12ab^2c/18ab^3c^2f

$$\frac { 3 a c ^ { 3 } f ^ { 3 } } { 8 a ^ { 2 } b c f ^ { 4 } } \cdot \frac { 12 a b ^ { 2 } c } { 18 a b ^ { 3 } c ^ { 2 } f }$$

Evaluate

$$\frac{c}{4a\left(bf\right)^{2}}$$

Solution Steps

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

$$\frac{3c^{2}}{8abf}\times \frac{12ab^{2}c}{18ab^{3}c^{2}f}$$

Cancel out 6acb^{2} in both numerator and denominator.

$$\frac{3c^{2}}{8abf}\times \frac{2}{3bcf}$$

Multiply \frac{3c^{2}}{8abf} times \frac{2}{3bcf} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3c^{2}\times 2}{8abf\times 3bcf}$$

Cancel out 2\times 3c in both numerator and denominator.

$$\frac{c}{4abbff}$$

Multiply b and b to get b^{2}.

$$\frac{c}{4ab^{2}ff}$$

Multiply f and f to get f^{2}.

$$\frac{c}{4ab^{2}f^{2}}$$

Differentiate w.r.t. c

$$\frac{1}{4a\left(bf\right)^{2}}$$