Attention, les réponses aux QCM de rattrapage ne rapportent que \( 25 \% \) des points. \[ f: x \mapsto\left(-4 x^{4}-5 x\right)^{4} \] Quelle est la dérivée de la fonction \( f \) ? On admettra qu'un ensemble de dérivabilité existe pour cette fonctio \[ 1 \]

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

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

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

Find the first and second derivatives of \( f(x)=x^{3}(2 x-5) \)

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