Evaluate: \(\underset { x\rightarrow 0 }{ lim } \frac { \sin { 3x } }{ \sin { 5x } } \)

Show that \(\underset { x\rightarrow 0 }{ lim } \frac { \log { \left( 1+{ x }^{ 2 } \right) } }{ \sin ^{ 3 }{ x } } =1\)

Find \(\frac{d}{dx}(e^{3x})\) from first principle.

If y = \(\frac{1}{u^2}\) and u = x² - 9, then find \(\frac{dy}{dx}\).

If x³ + y³ = 3axy, then find \(\frac{dy}{dx}\).