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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

Note:

  1. Sum, difference,product and quotient of two differentiable functions is differentiable.
  2. The composition of differentiable function is also a differentiable function.
April 18, 2019
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