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All of the standard functions are differentiable except at certain singular points, as follows:
Polynomials are differentiable for all arguments.
A rational function is differentiable except where , where the function grows to infinity. This happens in two ways, illustrated by and .
Sines and cosines and exponents are differentiable everywhere but tangents and secants are singular at certain values. (Where?)
The inverse functions to powers such as and are differentiable where they are defined except where the functions they are inverse to have 0 derivative.
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