====== Unit 02: Differentiation ======
Here is the list of important questions.
<list-group>
  * Differentiate $\frac{(x^2+1)^2}{x^2-1}$ $w.r.t.x$. --- // BSIC Gujranwala (2016)//
  * If $x=at^2$, $y=2at$. Find $\frac{dy}{dx}$  --- // BSIC Gujranwala (2016)//
  * Differentiate $x^2-\frac{1}{x^2}$ $w.r.t.x^2$. --- // BSIC Gujranwala (2016)//
  * Prove that $\frac{d}{dx}(tan^{-1}x)=\frac{1}{1+x^2}$  --- // BSIC Gujranwala (2016)//
  * Prove that $\frac{d}{dx}(sinh^{-1}x)=\frac{1}{\sqrt{1+x^2}}$  --- // BSIC Gujranwala (2016)//
  * If $y=x^2ln(\frac{1}{x})$. Find $\frac{dy}{dx}$.  --- // BSIC Gujranwala (2016)//
  * If $x=sin\theta$, $y=sin m\theta$. Find $\frac{dy}{dx}$.  --- // BSIC Gujranwala (2016)//
  * Apply Maclaurin series to expand $cosx =1-\frac{x^2}{2!}$ --- // BSIC Gujranwala (2016)//
  * Differentiate $cos^2x$ $w.r.t.sin^2x$. --- // BSIC Gujranwala (2016)//
  * Using differential find $\frac{dy}{dx}$, When $x^2+2y^2=16$ --- // BSIC Gujranwala (2016)//
  * Show that $\frac{dy}{dx}=\frac{y}{x}$ if $\frac{y}{x}=tan^{-1}(\frac{x}{y})$ --- // BSIC Gujranwala (2016)//
  * Find $\frac{dy}{dx}$, if $y^2-xy-x^2+4=0$ --- // BSIC Gujranwala (2015)//
  * Prove that $\frac{dy}{dx}({log_a}^x)=\frac{1}{x \ln a}$ --- // BSIC Gujranwala (2015)//
  * Find $\frac{dy}{dx}$, if $y=(\ln x)^{\ln x}$ --- // BSIC Gujranwala (2015)//
  * Find $y_4$ if $y=\cos ^3x$ --- // BSIC Gujranwala (2015)//
  * Expand $a^x$ in Meclaurin series. --- // BSIC Gujranwala (2015)//
  * Prove that derivative of a constant is zero. --- // BSIC Gujranwala (2015)//
  * Determine the interval in which $f$ is increasing if $f(x)=x^3-6x^2+9x$. --- // BSIC Gujranwala (2015)//
  * Differentiate $\cos \sqrt{x}+\sqrt{\sin x}$ with respect to $x$. --- // BSIC Gujranwala (2015)// 
  * Use differentials to approximate the value of $(31)^{\frac{1}{5}}$ --- // BSIC Gujranwala (2015)//
  * If $y=x^4+2x^2+2$, prove that $\frac{dy}{dx}=40x\sqrt{y-1}$--- // BSIC Gujranwala (2015)//
  * Find $\frac{dy}{dx}$, if $x=\frac{a(1-t^2)}{1+t^2}$ and $y=\frac{2bt}{1+t^2}$. --- // BSIC Gujranwala (2015)//
  * Differentiate $\cos \sqrt{x}$ with respect to $x$ by ab-initio method. --- // BSIC Gujranwala (2015)//
  * A box with a square base and open top is to have avolume of $4$ cubic dm. Find the dimensions of the box which will require the least material? -- // BSIC Gujranwala (2015)//
  * Find the extreme values of the function $f(x)=\sin x +\cos x$ occurring in the intial $[0,2\pi]$ -- // BSIC Gujranwala (2015)//
  * Find $\frac{dy}{dx}$, if $x^2-4xy-5y^2=0$ --- // FBSIC (2016)//
  * If $y=\sqrt{\tan x+\sqrt{\tan x+\sqrt{x}}+...}$, prove that $(2y-1)\frac{dy}{dx}=\sec ^2x$. --- // FBSIC (2016)//
  * Find $\frac{dy}{dx}$, if $y=x e^{\sin x}$.  --- // FBSIC (2016)//
  * Show that $\frac{dy}{dx}=\frac{y}{x}$, if $\frac{y}{x}=\tan ^{-1}\frac{y}{x}$. --- // FBSIC (2016)//
  * Differentiate $(\sqrt{x}-\frac{1}{\sqrt{x}})$ w.r.t. $x$.--- // BSIC Rawalpandi (2017)//
  * Find $\frac{dy}{dx}$, if $y=\sqrt{x+\sqrt{x}}$.--- // BSIC Rawalpandi (2017)//
  * Differentiate $x^2 \sec 4x$ w.r.t. $x$..--- // BSIC Rawalpandi (2017)//
  * Find $\frac{dy}{dx}$, if $x=y \sin y$.--- // BSIC Rawalpandi (2017)//
  * Find $f'(x)$ if $f(x)=x^2 \ln \sqrt{x}$--- // BSIC Rawalpandi (2017)//
  * Find $y_2$ if $y-\cos ^3x$.--- // BSIC Rawalpandi (2017)//
  * Find $\frac{dy}{dx}$, if $y=x e^{\sin x}$.--- // BSIC Rawalpandi (2017)//
  * Apply maclaurin`s series expansions to prove that $e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+...$--- // BSIC Rawalpandi (2017)//
  * Determine the intervals in which $f(x)=\cos x: x\in (-\frac{\pi}{2},\frac{\pi}{2})$ is increasing or decreasing function.--- // BSIC Rawalpandi (2017)//
  * If $x=\sin \theta, \gamma=\sin (m\theta)$, then prove that $(1-x^2)y_2-xy_1+m^2y+0$--- // BSIC Rawalpandi (2017)//
  * Using differential, find $\frac{dy}{dx}$ in the equation $x^2+2y^2=16$--- // BSIC Rawalpindi(2017)//
  * If $f(x)=x^2$, then find $f'(x)$ by defination. --- // BSIC Sargodha(2016)//
  * Differentiate $\frac{a+x}{a-x}$ w.r.t.$x$.--- // BSIC Sargodha(2016)//
  * If $x=\theta +\frac{1}{\theta}$ and $y=\theta +1$ then find $\frac{dy}{dx}$. --- // BSIC Sargodha(2016)//
  * find $\frac{dy}{dx}$ if $y=x \cos y$  --- // BSIC Sargodha(2016)//
  * If $y=e^{x^2+1}$ then find $\frac{dy}{dx}$. --- // BSIC Sargodha(2016)//
  * Find $f'(x)$, if $f(x)=\ln (e^x+e^{-x})$. --- // BSIC Sargodha(2016)//
  * If $y=\cos (ax+b)$ then find $y_1$. --- // BSIC Sargodha(2016)//
  * By maclaurin`s series, prove that $e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+...$. --- // BSIC Sargodha(2016)//
  * Defined increasing and decreasing function. --- // BSIC Sargodha(2016)//
  * Prove that $y \frac{dy}{dx}+x=0$ if $x=\frac{1-t^2}{1+t^2}$, $y==\frac{2t}{1+t^2}$ . --- // BSIC Sargodha(2016)//
  * Define the derivative w.r.t.$x$. --- // BSIC Sargodha(2017)//
  * Differentiate w.r.t.$x$ $(x-5)(3-x)$  --- // BSIC Sargodha(2017)//
  * Differentiate w.r.t.$x$ $\frac{1}{a}\sin ^{-1}\frac{a}{x}$  --- // BSIC Sargodha(2017)//
  * Find $\frac{dy}{dx}$, if $y=x^2 \ln \sqrt{x}$ --- // BSIC Sargodha(2017)//
  * Find $\frac{dy}{dx}$, if $y=xe^{\sin x}$ --- // BSIC Sargodha(2017)//
  * Find $y_2$ if $y=(2x+5)^{\frac{1}{2}}$ --- // BSIC Sargodha(2017)//
  * What is the decreasing function. --- // BSIC Sargodha(2017)//
  * Find $\frac{dy}{dx}$, if $y= \ln \sqrt{\frac{x^2-1}{x^2+1}}$ --- // BSIC Sargodha(2017)//
  * Differentiate $\cos \sqrt{x}$ w.r.t.$x$ from first principle. --- // BSIC Sargodha(2017)//




</list-group>
{{tag>FSc FSc_Part2 Important_Questions_FSc_2}}