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Worksheet
Super-Speed Differentiation (HL)
IB Mathematics AA · HL · Shadow Worksheet
Practice
Name
Question 1
Differentiate all of the following as quickly as possible:
(a)\(f(x)=x^2\sin x\)
(b)\(f(x)=\dfrac{\ln x}{x^2}\)
(c)\(f(x)=e^{\sin x}\)
(d)\(f(x)=\sin^3(2x)\)
(e)\(f(x)=\ln(\cos x)\)
(f)\(f(x)=\dfrac{e^x}{1+e^x}\)
(g)\(f(x)=x^2e^{-x^2}\)
(h)\(f(x)=rctan(2x)\) (HL: recall \(\dfrac{d}{dx}rctan x=\dfrac{1}{1+x^2}\))
(a)
Answer
\(2x\sin x+x^2\cos x\)
(b)
Answer
\(\dfrac{ frac{1}{x}\cdot x^2-2x\ln x}{x^4}=\dfrac{1-2\ln x}{x^3}\)
(c)
Answer
\(\cos x\cdot e^{\sin x}\)
(d)
Answer
\(6\sin^2(2x)\cos(2x)\)
(e)
Answer
\(\dfrac{-\sin x}{\cos x}=- an x\)
(f)
Answer
\(\dfrac{e^x(1+e^x)-e^{2x}}{(1+e^x)^2}=\dfrac{e^x}{(1+e^x)^2}\)
(g)
Answer
\(2xe^{-x^2}-2x^3e^{-x^2}=2xe^{-x^2}(1-x^2)\)
(h)
Answer
\(\dfrac{2}{1+4x^2}\)
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