Solve -3/5a5a^4/7b^5b^3/2a^2

$$- \frac{ 3 }{ 5a } \frac{ 5 { a }^{ 4 } }{ 7 { b }^{ 5 } } \frac{ { b }^{ 3 } }{ 2 { a }^{ 2 } }$$

Evaluate

$$-\frac{3a}{14b^{2}}$$

Solution Steps

Multiply -\frac{3}{5a} times \frac{5a^{4}}{7b^{5}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 5a^{4}}{5a\times 7b^{5}}\times \frac{b^{3}}{2a^{2}}$$

Cancel out 5a in both numerator and denominator.

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

Multiply \frac{-3a^{3}}{7b^{5}} times \frac{b^{3}}{2a^{2}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply 2 and 7 to get 14.

$$\frac{-3a}{14b^{2}}$$

Differentiate w.r.t. a

$$-\frac{3}{14b^{2}}$$