Question

what is the derivative of sec^-1x w.r.t. x if x<-1​

Answer 1

Answer:

$\frac{dy}{dx} { \sec }^{ - 1} x \\ \\ = \frac{1}{x \sqrt{ {x}^{2} + 1} } \\ \\ = \frac{1}{ - x \sqrt{ {( - x)}^{2} + 1 }} \: \: \: (cause \: \: x < - 1)\\ \\ = - \frac{1}{x \sqrt{ {x}^{2} + 1 } }$