Question:
$\frac{d}{dx}\left(tan^{-1}\left(\frac{\sqrt{x}-\sqrt{a}}{1+\sqrt{xa}}\right)\right)$, $x$, $a > 0$, is
$\frac{d}{dx}\left(tan^{-1}\left(\frac{\sqrt{x}-\sqrt{a}}{1+\sqrt{xa}}\right)\right)$, $x$, $a > 0$, is
Updated On: Jul 6, 2022
- $tan^{-1}\sqrt{x}+tan^{-1}\sqrt{a}$
- $\frac{1}{1+x}$
- $\frac{1}{1+x}+\frac{1}{1+a}$
- $\frac{1}{2\sqrt{x}\left(1+x\right)}$
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The Correct Option is D
Solution and Explanation
Answer (d) $\frac{1}{2\sqrt{x}\left(1+x\right)}$
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Notes on Continuity and differentiability
Concepts Used:
Continuity & Differentiability
Definition of Differentiability
f(x) is said to be differentiable at the point x = a, if the derivative f ‘(a) be at every point in its domain. It is given by
Definition of Continuity
Mathematically, a function is said to be continuous at a point x = a, if
It is implicit that if the left-hand limit (L.H.L), right-hand limit (R.H.L), and the value of the function at x=a exist and these parameters are equal to each other, then the function f is said to be continuous at x=a.
If the function is unspecified or does not exist, then we say that the function is discontinuous.