The curve C C\,C has the equation
x=2tan2yx = 2\tan 2yx=2tan2y, where −π4<y<π4\displaystyle -\frac{\pi}{4} < y < \frac{\pi}{4}−4π<y<4π
You may use the result ddu(tanku)=ksec2ku\dfrac{d}{du}(\tan ku) = k\sec^2 kudud(tanku)=ksec2ku.
Show that, for all points (x,y)(x, y)(x,y) lying on CCC,
dydx=ax2+b\displaystyle \frac{dy}{dx} = \frac{a}{x^2 + b}dxdy=x2+ba
where a a\,a and b b\,b are constants to be found.
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.