Techniques of Differentiation

2021 SAJC Promo Q5 (a) (i) Show that $frac{text{d}}{text{d}x}left( {{3}^{2x}} right)={{9}^{x}}ln 9$. (ii) Hence, differentiate ${{tan }^{-1}}left( {{3}^{2x}} right)$, $x>0$ with respect to $x$. (b) Given that ${{y}^{2y}}={{e}^{3x+2e}}$, where $y>{{e}^{-1}}$,

2011 MJC P2 Q4 (a) (i) The equation of a curve is given by ${{e}^{x+y}}+e={{left( 2y-1 right)}^{2}}$. Find $frac{text{d}y}{text{d}x}$. [4] (ii) Write down an equation relating $x$ and $y$ at

Basics of Differentiation Techniques Q2 Find $frac{text{d}y}{text{d}x}$ in terms of $x$ and $y$ if (a) $x+sqrt{xy}=3$ (b) ${{x}^{n}}+{{y}^{n}}=kxy$ , where $n$ and $k$ are constants. Suggested Handwritten and Video Solutions

2014 Promo CJC Q2 The variables $x$ and $y$ are related by ${{3}^{y}}=xy-sec x$. Find $frac{text{d}y}{text{d}x}$ in terms of $x$ and $y$. [4] Suggested Handwritten and Video Solutions

2013 Promo CJC Q4 (a) Given that $y={{tan }^{-1}}sqrt{x}$, find $frac{text{d}y}{text{d}x}$. [2] (b) Given that $sqrt[x]{y}=sqrt[y]{x}$, where $x>0$, $y>0$, find $frac{text{d}y}{text{d}x}$ . [4] Suggested Handwritten and Video Solutions (a) (b)

2012 Promo CJC Q11 (b) Given that $y={{left( 2x+1 right)}^{x}}$ for $x>0$, find $frac{text{d}y}{text{d}x}$. [3] Suggested Handwritten and Video Solutions

2010 MJC P2 Q4 (a) The variables $x$ and $y$ are related by $y=sqrt{x}+ln {{left( xy right)}^{3}}$. Find the value of $frac{text{d}y}{text{d}x}$ when both $x$ and $y$ are equal to

2013 YJC Promo Q4 (a) It is given that ${{y}^{x}}={{e}^{y}}{{x}^{2}}$ . Find $frac{text{d}y}{text{d}x}$in terms of $x$ and $y$, simplifying your answer. [4] Suggested Handwritten and Video Solutions

Inverse-trigonometric function derivative Q1 Find and simplify the derivatives of the following functions: (a) ${{tan }^{-1}}left( frac{1}{sqrt{x}} right)$ (b) ${{sin }^{-1}}sqrt{1-{{x}^{2}}}$ (c) ${{cos }^{-1}}left( {{e}^{-{{x}^{2}}}} right)$ Suggested Handwritten and Video