Solve frac{4a^{4}b^{3}c}{5ad^{3}}*3bd^2/8a^2cdivb^4/2ac^3

$$\frac { 4 a ^ { 4 } b ^ { 3 } c } { 5 a d ^ { 3 } } \times \frac { 3 b d ^ { 2 } } { 8 a ^ { 2 } c } \div \frac { b ^ { 4 } } { 2 a c ^ { 3 } }$$

Evaluate

$$\frac{3a^{2}c^{3}}{5d}$$

Short Solution Steps

Cancel out a in both numerator and denominator.

$$\frac{\frac{4ca^{3}b^{3}}{5d^{3}}\times \frac{3bd^{2}}{8a^{2}c}}{\frac{b^{4}}{2ac^{3}}}$$

Multiply \frac{4ca^{3}b^{3}}{5d^{3}} times \frac{3bd^{2}}{8a^{2}c} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4ca^{3}b^{3}\times 3bd^{2}}{5d^{3}\times 8a^{2}c}}{\frac{b^{4}}{2ac^{3}}}$$

Cancel out 4ca^{2}d^{2} in both numerator and denominator.

$$\frac{\frac{3abb^{3}}{2\times 5d}}{\frac{b^{4}}{2ac^{3}}}$$

Divide \frac{3abb^{3}}{2\times 5d} by \frac{b^{4}}{2ac^{3}} by multiplying \frac{3abb^{3}}{2\times 5d} by the reciprocal of \frac{b^{4}}{2ac^{3}}.

$$\frac{3abb^{3}\times 2ac^{3}}{2\times 5db^{4}}$$

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

$$\frac{3aac^{3}}{5d}$$

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

$$\frac{3a^{2}c^{3}}{5d}$$

Differentiate w.r.t. d

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