Solve 8a^{frac{1/2}-27b^{1/2}}{2a^{1/2}+3b^{1/2}}*frac{4a-9b}{4a+6a^frac{1{2}}b^frac{1{2}}+9b}+12a^frac{1{2}}b^frac{1{2}}

$$\frac { 8 a ^ { \frac { 1 } { 2 } } - 27 b ^ { \frac { 1 } { 2 } } } { 2 a ^ { \frac { 1 } { 2 } } + 3 b ^ { \frac { 1 } { 2 } } } \cdot \frac { 4 a - 9 b } { 4 a + 6 a ^ { \frac { 1 } { 2 } } b ^ { \frac { 1 } { 2 } } + 9 b } + 12 a ^ { \frac { 1 } { 2 } } b ^ { \frac { 1 } { 2 } }$$

Evaluate

$$\frac{48\sqrt{b}a^{\frac{3}{2}}+108\sqrt{a}b^{\frac{3}{2}}+72ab-78\sqrt{ab}+16a+81b}{6\sqrt{ab}+4a+9b}$$

Differentiate w.r.t. a

$$\frac{6\left(48a^{\frac{3}{2}}\sqrt{ab}+54b^{\frac{3}{2}}\sqrt{ab}+180b\sqrt{ba^{2}}+54\sqrt{a}b^{2}-32\sqrt{b}a^{2}+48ba^{\frac{3}{2}}-72ab^{\frac{3}{2}}+81b^{\frac{5}{2}}+68\sqrt{ba^{2}}-30\sqrt{a}b-34\sqrt{b}a-99b^{\frac{3}{2}}\right)}{\sqrt{a}\left(6\sqrt{ab}+4a+9b\right)^{2}}$$