The function f f\,f is defined by f(x)=1−2(x+4)+x−8(x−2)(x+4),x∈R,x≠−4,x≠2\displaystyle f(x) = 1 - \frac{2}{(x+4)} + \frac{x-8}{(x-2)(x+4)}, x \in \mathbb{R}, x \neq -4, x \neq 2f(x)=1−(x+4)2+(x−2)(x+4)x−8,x∈R,x=−4,x=2. Show that f(x)=x−3x−2\displaystyle f(x) = \frac{x-3}{x-2}f(x)=x−2x−3.
The function g g\,g is defined by g(x)=ex−3ex−2,x∈R,x≠ln2\displaystyle g(x) = \frac{e^x - 3}{e^x - 2}, x \in \mathbb{R}, x \neq \ln 2g(x)=ex−2ex−3,x∈R,x=ln2. Differentiate g(x)g(x)g(x) to show that g′(x)=ex(ex−2)2\displaystyle g'(x) = \frac{e^x}{(e^x - 2)^2}g′(x)=(ex−2)2ex.
Find the exact values of x x\,x for which g′(x)=1g'(x) = 1g′(x)=1.
Practise Edexcel A Level Old Maths Differentiation with exam-style questions for A Level Old Maths. 14 questions, matched to the Edexcel A Level Old Maths (9371) specification and written in Unit exams C1, C2, C3 and C4 plus two applied units (e.g. S1 and M1) style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.