Differentiate the following w.r.t. x: log(cos ex)
Solution and Explanation
Let y=log(cos ex)
By using the chain rule, we obtain
\(\frac{dy}{dx}=\frac{d}{dx}[log(cos e^x]\)
=\(\frac{1}{cose^x}.\frac{d}{dx}(cose^x)\)
=\(\frac{1}{cose^x}.(-sin e^x).\frac{d}{dx}(e^x)\)
=\(\frac{-sin e^x}{cos e^x}.e^x\)
=-\(e^x tan e^x,e^x\)≠\((2n+1)\frac{\pi}{2},\)\(nεN\)
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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.