Some Standard Results on Differentiability

Functions f(x)	Intervals in which f(x) is differentiable
1. Polynomial	$\displaystyle \left( -\infty , \infty \right)$
2. Exponential $\displaystyle \left( { a }^{ x },a>0 \right)$	$\displaystyle \left( -\infty , \infty \right)$
3. Constant	$\displaystyle \left( -\infty ,\infty \right)$
4. Logarithmic	Each Point in its domain
5. Trigonometric	Each Point in its domain
6. Inverse Trigonometric	Each Point in its domain

Sum, difference,product and quotient of two differentiable functions is differentiable.
The composition of differentiable function is also a differentiable function.

April 18, 2019

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