Question

$A:\frac{d}{dx}\left(\sin x\right)atx=\frac{\pi }{2}$

$B:\frac{d}{dx}\left({\tan }^{-1}x\right)$ at $x=1$

$C:\frac{d}{dx}\left(e^x\right)$ at $x=0$

$D:\frac{d}{dx}\left(x^x\right)atx=e$

Arrangement of the above values in the increasing order of the magnitude

• A. B, C, A, D
• B. D, A, B, C
• C. D, B, C, A
• D. A, B, C, D

Answer 1

The correct option is D A, B, C, D

$A.\frac{d}{dx}\left(sinx\right)=cosx$

Put $x=\frac{\pi }{2}$

$=0$

$B.\frac{d}{dx}\left(ta{n}^{-1}x\right)=\frac{1}{1+x^2}$

Put$x=1$

$=\frac{1}{2}$

$C.\frac{d}{dx}\left(e^x\right)=e^x$

Put $x=0$

$=1$

$D.\frac{d}{dx}\left(x^x\right)=\frac{d}{dx}\left(e^{xLogx}\right)=x^x(Logx+1)$

$=2e^e$