Question

$${ \left( \frac{ 2 }{ 3 } \right) }^{ x } \times { \left( \frac{ 3 }{ 2 } \right) }^{ x } \times { \left( \frac{ 2 }{ 3 } \right) }^{ 6 } \times { \left( \frac{ 2 }{ 3 } \right) }^{ -2x }$$

Evaluate

$\frac{64\times \left(\frac{9}{4}\right)^{x}}{729}$

Differentiate w.r.t. x

$\frac{64\ln(\frac{9}{4})\times \left(\frac{9}{4}\right)^{x}}{729}$