Answer
${\frac{d{csc^{-1}{u}}}{du}}$ = -${\frac{1}{|u|{\sqrt{({(u^2-1)})}}}}$
Work Step by Step
${csc^{-1}{u}}$ value determined by the given equation:
${csc^{-1}{u}}$ = ${\frac{\pi}{2}}-{sec^{-1}{u}}$
on differentiating both sides:
${\frac{d{csc^{-1}{u}}}{du}}={\frac{d\pi}{2du}}-{\frac{d{sec^{-1}{u}}}{du}}$
differentiation of constant is zero:
and ${\frac{d{\sec^{-1}{u}}}{du}={\frac{1}{|u|{\sqrt{({(u^2-1)})}}}}}$
so ${\frac{d{csc^{-1}{u}}}{du}}$ = -${\frac{1}{|u|{\sqrt{({(u^2-1)})}}}}$
thus the final answer is: ${\frac{d{csc^{-1}{u}}}{du}}$ = -${\frac{1}{|u|{\sqrt{({(u^2-1)})}}}}$
