Question

If $y={\sec }^{-1}x,$ then $\frac{dy}{dx}$ is equal to

• A. $\frac{1}{x\sqrt{x^2+1}}$
• B. $\frac{1}{\sqrt{x^2-1}}$
• C. $\frac{1}{x\sqrt{1-x^2}}$
• D. $\frac{1}{x\sqrt{x^2-1}}$

Answer 1

Answer: (D)

$y={\sec }^{-1}x$
On differentiating w.r.t. $x,$
we get $\frac{dy}{dx}=\frac{1}{x\sqrt{x^2-1}}$