Question:
Differential coefficient of $\sqrt{sec\sqrt{x}}$ is
Differential coefficient of $\sqrt{sec\sqrt{x}}$ is
Updated On: Jul 6, 2022
- $\frac{1}{4\sqrt{x}}sec\sqrt{x}\,sin\sqrt{x}$
- $\frac{1}{4\sqrt{x}}\left(sec\sqrt{x}\right)^{3/2}\cdot sin\sqrt{x}$
- $\frac{1}{2}\sqrt{x}sec\sqrt{x}sin\sqrt{x}$
- $\frac{1}{2}\sqrt{x}\left(sec\sqrt{x}\right)^{3/2}\cdot sin\sqrt{x}$
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The Correct Option is B
Solution and Explanation
Let $y=\sqrt{sec\sqrt{x}}$
Differentiating $w$.$r$.$t$. $x$, we get
$\frac{dy}{dx}=\frac{1}{2\sqrt{sec\sqrt{x}}}\cdot sec\sqrt{x}\cdot tan\sqrt{x}\cdot\frac{1}{2\sqrt{x}}$
$=\frac{1}{4\sqrt{x}}\left(sec\sqrt{x}\right)^{1/2} \frac{sin\sqrt{x}}{cos\sqrt{x}}$
$=\frac{1}{4\sqrt{x}}\left(sec\sqrt{x}\right)^{3/2}\cdot sin\sqrt{x}$
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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.