Question

root of secant x minus 1 by secant X + 1 then DY by DX is equals to

Answer 1

Dear Student
$$\begin{gathered} \frac{d\frac{\sec \left(x-1\right)}{\sec \left(x+1\right)}}{dx}=\frac{d}{dx}\left(\cos (1+x)sec(1-x)\right)=\cos (1+x)\frac{d}{dx}\left(sec\right(1-x\left)\right)+sec(1-x)\frac{d}{dx}\left(\cos \right(1+x\left)\right) \\ =\cos (1+x)sec(1-x)\tan (1-x)(-1)+sec(1-x)(-\sin (1+x\left)\right) \\ =-sec(1-x)\left\{\sin (1+x)+\cos (1+x)\tan (1-x)\right\} \end{gathered}$$
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