d/dx arcsin(sqrt(x)) =
A1/(2 sqrt(x) × sqrt(1-x)) (chain rule)
Bln(x)
C1/sqrt(1-x)
D1/sqrt(x(1-x))
Answer & Solution
Correct answer: A. 1/(2 sqrt(x) × sqrt(1-x)) (chain rule)
d/dx arcsin(u) = (1/sqrt(1-u²)) du/dx with u = sqrt(x). du/dx = 1/(2 sqrt(x)). 1 - u² = 1 - x. So derivative = 1/[2 sqrt(x) sqrt(1-x)].
Related questions
The value of $ in(\tan^{-1}(3/4))$ is:The value of $\cos^{-1}(-1)$ is:For $x \in [-1, 1]$, the identity $ in^{-1}x + \cos^{-1}x$ equals:The principal value of $ in^{-1}(1/2)$ is:All real $x$ satisfying $ in^{-1}(x) + in^{-1}(1-x) = \cos^{-1}(x)$ areFor $x = -2$, the value of $\tan^{-1}\left(\dfrac{2x}{1-x^2}\right)$ equals$\displaystyle um_{n=1}^{\infty} \tan^{-1}\left(\frac{1}{n^2 + n + 1}\right)$ equals$\tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) = $