Question

$Iff\left(x\right)=ta{n}^{-1}\left(\frac{cosx-sinx}{cosx+sinx}\right),then{f}^{\prime }\left(0\right)=$

• A. 1
• B. 2
• C. -1
• D. -2

Answer 1

The correct option is C

-1

$f\left(x\right)=ta{n}^{-1}\left(\frac{cosx-sinx}{cosx+sinx}\right)=ta{n}^{-1}\left(tan(\frac{\pi }{4}-x)\right)=\frac{\pi }{4}-x{f}^{\prime }\left(x\right)=-1f^{\prime }\left(0\right)=-1$