Question:
If $y=e^{\frac{1}{2}log\left(1+tan^{2}\,x\right)}$, then $\frac{dy}{dx}$ is equal to
If $y=e^{\frac{1}{2}log\left(1+tan^{2}\,x\right)}$, then $\frac{dy}{dx}$ is equal to
Updated On: Jul 6, 2022
- $\frac{1}{2}sec^{2}x$
- $sec^{2}x$
- $secx\,tanx$
- $e^{\frac{1}{2}log\left(1+tan^{2}\,x\right)}$
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The Correct Option is C
Solution and Explanation
$y=e^{\frac{1}{2}log\left(1+tan^{2}\,x\right)}$
$=\left(sec^{2}\,x\right)^{1/2}=sec\,x$
$\therefore \frac{dy}{dx}=sec\,x\,tan\,x$
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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.