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\begin{question}{Physics:differentiatione1}
If y= $\frac{(1-x)^{2}}{x^{2}}$ then $\frac{dy}{dx}$ is
    \begin{multicols}{2}
        \begin{choices}
           \wrongchoice{$\frac{2}{x^{2}}+\frac{2}{x^{3}}$}
           \correctchoice{$\frac{2}{x^{2}}-\frac{2}{x^{3}}$}
           \wrongchoice{$-\frac{2}{x^{2}}-\frac{2}{x^{3}}$}
           \wrongchoice{$-\frac{2}{x^{2}}+\frac{2}{x^{3}}$}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione16}
    If $y=\sin(\sqrt{\sin x+\cos x})$, then $\frac{dy}{dx}=$
    \begin{multicols}{2}
        \begin{choices}[o]
           \wrongchoice{$\frac{1}{2}\frac{\cos(\sqrt{\sin x+\cos x})}{\sqrt{\sin x+\cos x}}$}
           \wrongchoice{$\frac{\cos(\sqrt{\sin x+\cos x})}{\sqrt{\sin x+\cos x}}$}
           \correctchoice{$\frac{1}{2}\frac{\cos(\sqrt{\sin x+\cos x})}{\sqrt{\sin x+\cos x}}(\cos x-\sin x)$}
           \wrongchoice{None of these}
        \end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione15}
    $\frac{d}{dx}\cos(\sin x^{2})=$
    \begin{multicols}{2}
        \begin{choices}[o]
           \wrongchoice{$\sin(\sin x^{2}).\cos x^{2}.2x$}
           \correctchoice{$-\sin(\sin x^{2}).\cos x^{2}.2x$}
           \wrongchoice{$-\sin(\sin x^{2}).\cos^{2}x.2x$}
           \wrongchoice{None of these.}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione14}
    $\frac{d}{dx}[\sin^{n}x\cos nx]=$
    \begin{multicols}{2}
        \begin{choices}
           \wrongchoice{$n\sin^{n-1}x\cos(n)x$}
           \correctchoice{$n\sin^{n-1}x\cos(n+1)x$}
           \wrongchoice{$n\sin^{n-1}x\cos(n-1)x$}
           \wrongchoice{$n\sin^{n-1}x\sin(n+1)x$}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione13}
If $y=\cos (\sin x^{2})$, then at x=$\sqrt{\frac{\pi}{2}}, \frac{dy}{dx}$=
    \begin{multicols}{2}
        \begin{choices}
           \wrongchoice{$-2$}
           \correctchoice{$0$}
           \wrongchoice{$2$}
           \wrongchoice{$-2\sqrt{\frac{\pi}{2}}$}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione12}
$\frac{d[cos(1-x^{2})^{2}]}{dx}$=
    \begin{multicols}{2}
        \begin{choices}
           \wrongchoice{$-2x(1-x^{2})sin(1-x^{2})^{2}$}
           \correctchoice{$4x(1-x^{2})sin(1-x^{2})^{2}$}
           \wrongchoice{$-4x(1-x^{2})sin(1-x^{2})^{2}$}
           \wrongchoice{$-2(1-x^{2})sin(1-x^{2})^{2}$}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione11}
If $y=a\sin x+b\cos x$, then $y^{2}+(\frac{dy}{dx})^{2}$ is a 
    \begin{multicols}{2}
        \begin{choices}
           \wrongchoice{Function of x}
           \correctchoice{constant}
           \wrongchoice{Function of x and y}
           \wrongchoice{Function of y}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione10}
If $\sin y+e^{-x\cos y}=e$, then $\frac{dy}{dx}$ =
    \begin{multicols}{2}
        \begin{choices}
           \wrongchoice{$\sin y$}
           \correctchoice{$e$}
           \wrongchoice{$-x\cos y$}
           \wrongchoice{$\sin y-x\cos y$}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione9}
If $y=\sec x^{o}$ ,then $\frac{dy}{dx}$ = 
    \begin{multicols}{2}
        \begin{choices}
           \wrongchoice{$\sec x.\tan x$}
           \correctchoice{$\frac{\pi}{180}\sec x^{o}\tan x^{o}$}
           \wrongchoice{$\frac{180}{\pi}\sec x^{o}\tan x^{o}$}
           \wrongchoice{$\sec x^{o}\tan x^{o}$}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione8}
$\frac{d(sin2x^{2})}{dx}$ equals
    \begin{multicols}{2}
        \begin{choices}
           \wrongchoice{$2sinx^{2}\cos x^{2}$}
           \correctchoice{$4x\cos(2x^{2})$}
           \wrongchoice{$4xsinx^{2}$}
           \wrongchoice{$4xsinx^{2}.cosx^{2}$}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione7}
The derivative of $F[f\{\phi(x)\}]$ is
    \begin{multicols}{2}
        \begin{choices}
           \wrongchoice{$F'[f\{\phi(x)\}]$}
           \correctchoice{$F'[f\{\phi(x)\}]f'\{\phi(x)\}\phi'(x)$}
           \wrongchoice{$F'[f\{\phi(x)\}]f'[\phi(x)]$}
           \wrongchoice{$F'[f\{\phi(x)\}]f[\phi(x)]$}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione6}
The derivative of $f(x)=x|x|$ is	
    \begin{multicols}{2}
        \begin{choices}
           \wrongchoice{$2x$}
           \correctchoice{$2|x|$}
           \wrongchoice{$-2x$}
           \wrongchoice{$2x^{2}$}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione5}
If y= $\sqrt{\frac{(1+x)}{(1-x)}}$ , then $\frac{dy}{dx}$ = 
    \begin{multicols}{2}
        \begin{choices}
           \wrongchoice{$\frac{2}{(1+x)^{\frac{1}{2}}(1-x)^{\frac{3}{2}}}$}
           \correctchoice{$\frac{1}{(1+x)^{\frac{1}{2}}(1-x)^{\frac{3}{2}}}$}
           \wrongchoice{$\frac{1}{2(1+x)^{\frac{1}{2}}(1-x)^{\frac{3}{2}}}$}
           \wrongchoice{$\frac{2}{(1+x)^{\frac{3}{2}}(1-x)^{\frac{1}{2}}}$}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione4}
If $pv=81$, then $\frac{dp}{dv}$ is at $v=9$ equal to
    \begin{multicols}{2}
        \begin{choices}[o]
           \wrongchoice{1}
           \correctchoice{-1}
           \wrongchoice{2}
           \wrongchoice{None of these}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione3}
If $x=y\sqrt{1-y^{2}}$ , then $\frac{dy}{dx}$ = 
    \begin{multicols}{2}
        \begin{choices}
           \wrongchoice{$0$}
           \correctchoice{$\frac{\sqrt{1-y^{2}}}{1-2y^{2}}$}
           \wrongchoice{$x$}
           \wrongchoice{$\frac{\sqrt{1-y^{2}}}{1+2y^{2}}$}
    	\end{choices}
    \end{multicols}
\end{question}

\begin{question}{Physics:differentiatione2}
If $2t=v^{2}$,then $\frac{dv}{dt}$ is equal to
    \begin{multicols}{2}
        \begin{choices}
           \wrongchoice{$0$}
           \correctchoice{$\frac{1}{v}$}
           \wrongchoice{$\frac{1}{4}$}
           \wrongchoice{$\frac{1}{2}$}
    	\end{choices}
    \end{multicols}
\end{question}


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