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2012 ACJC Promo Q2 Differentiate the following with respect to $x$. (i) ${{cos }^{-1}}left( sin x right)$ where $frac{pi }{2}<x<frac{3pi }{2}$, [2] (ii) $ln sqrt{frac{{{e}^{x}}+1}{1-{{e}^{-x}}}}$ [3] Suggested Handwritten and Video
Basics of Differentiation Techniques Q1 Differentiate the following expressions with respect to $x$. (a) $frac{4{{x}^{3}}+2{{x}^{2}}+1}{x}$ (b) $text{cose}{{text{c}}^{3}}sqrt{x}$ (c) ${{cos }^{2}}left( x{}^circ right)+tan left( x{}^circ right)$ (d) $ln sqrt{frac{x-a}{x+a}}$ , where
2021 ASRJC Promo Q1 It is given that ${{y}^{2}}=sin x+cos x$. Show that $yfrac{{{text{d}}^{3}}y}{text{d}{{x}^{3}}}+Afrac{text{d}y}{text{d}x}frac{{{text{d}}^{2}}y}{text{d}{{x}^{2}}}+yfrac{text{d}y}{text{d}x}=0$, where $A$ is a real constant to be determined. [4] Suggested Handwritten and Video Solutions
2015 MI P2 Q2 [Two circles are concentric when they have the same centre but different radii.]Two concentric circles have radii $R$ and $r$, where $R>r$ . If $R$ increases
2013 TJC P2 Q1 The diagram below shows the points $P$ and $Q$ on the circumference of a circle with centre $O$, and radius $2a$ cm, where $angle POQ=theta $.
2010 TPJC P1 Q6 The diagram below shows the graph of $y=text{{f}’}left( x right)$intersecting the $x$-axis at $x=-3$ and $x=1$. Given that $text{f}left( -3 right)=4$ and $text{f}left( 1 right)=1$, (i)
2009 HCI P1 Q3 The diagram below shows the graph of $y=text{{f}’}left( x right)$. The curve passes through the origin and has turning points at $left( -3,0 right)$ and $left(
2020 TJC P1 Q1 Given that $A=sqrt{1+frac{1}{{{x}^{2}}}}$, and that the rate of decrease of $A$ is $k$ times the rate of increase of $x$ when $x=k$, find $k$, where $k$
2013 YJC P1 Q7 The equation of a curve is ${{y}^{2}}-xy=-1$. (i) Find the equations of all tangents to the curve that are parallel to the $y$-axis [4] (ii) State
2020 EJC Promo Q7 The curve $C$ has equation ${{tan }^{-1}}y=xln {{x}^{2}}-2x-y$, where $xin mathbb{R}$, $x>0$. (i) Show that $left( 2+{{y}^{2}} right)frac{text{d}y}{text{d}x}=2left( 1+{{y}^{2}} right)ln x$. [2] (ii) Hence find the