\( \int \sec ( 3 x ) \cdot \operatorname { Tgn } ( 3 x ) d x \)

Find the derivative of the function \( f(x)=-\frac{x^{3}}{x-1} \)

Solve the second order ordinary differential equation \[ \begin{array}{l}\left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}-2 x \frac{d y}{d x}+l(l+1) y=0 \\ \text { and with the knowledge that Legendre's polynomials are defined such that } \mathrm{P}_{1}(\mathrm{x}=1)=1 \text {, show that } \\ \qquad P_{2}(x)=\frac{1}{2}\left(3 x^{2}-1\right)\end{array} \]

\( f ( x ) = \sqrt { \frac { x } { r - x ^ { r } } } \)

Use the quotient rule to find the derivative of the following. \( y=\frac{4 x+9}{\sqrt{x}} \)

Use the quotient rule to find the derivative of the given function. \( f(t)=\frac{7 t^{2}-9 t}{9 t+5} \)