Question 1 - A-Level Maths

Exam Board	OCR
Module	C4 (Core Mathematics 4)
Topic	Implicit equations and differentiation

Differentiate each of the following with respect to $x$ and simplify your answers.
1. $\quad \ln ( \cos x )$
2. $x ^ { 2 } \sin 3 x$
3. A curve has the equation
$$x ^ { 2 } + 3 x y - 2 y ^ { 2 } + 17 = 0$$
Find an expression for $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $x$ and $y$.
Find an equation for the normal to the curve at the point ( $3 , - 2$ ).