Question:
If $y = \sec\, x^?$, then $\frac{dy}{dx}$ is equal to:
If $y = \sec\, x^?$, then $\frac{dy}{dx}$ is equal to:
Updated On: Apr 17, 2024
- $\sec\, x\, \tan \,x$
- $\sec \,x^?\, \tan \,x^?$
- $\frac{\pi}{180} \sec \,x^\circ \, \tan \, x^\circ$
- none of these
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The Correct Option is C
Solution and Explanation
Let $y = \sec\, x?$
Now ,$x^\circ = \frac{\pi}{180} . x \:\:\: \therefore \: y =\sec \frac{\pi}{180} x$
Now, $\frac{dy}{dx} = \frac{\pi}{180} \sec \frac{x \pi}{180} \tan \frac{\pi}{180} x$
$\Rightarrow \:\: \frac{dy}{dx} =\frac{\pi}{180} \: \sec \, x^\circ . \tan \, x^\circ$
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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.