Question

[d/dx sec⁻¹x]x=-3=.........,Select Proper option from the given options.
(a) 1/√x²-1
(b) - 1/√x²-1
(c) 1/6√2
(d) -1/6√2

Answer 1

I guessed your question is ----->
$\bf{\{\frac{d}{dx}sec^{-1}x\}x=-3}$

we know, differentiation of $sec^{-1}x$ is $\frac{1}{|x|\sqrt{x^2-1}}$

so, $\frac{d}{dx}sec^{-1}x=\frac{1}{|x|\sqrt{(x^2-1)}}$

or, $[\frac{d}{dx}sec^{-1}x]x=\frac{\pm1}{\sqrt{x^2-1}}=-3$

here we can see that 1/√(x² - 1) , -1/√(x² - 1) both are correct. because we can't choose anyone without condition of x.

hence,