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Derivative of trigonometric functions - tan(x)

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Description
Finding the derivative of trigonometric functions is an excellent exercise and requires application of basic principles of trigonometric identities of compound angles, a bit of algebraic simplification and regrouping and finally applying the limits.  it is not that difficult, but student often makes mistakes in simplification while carrying out the multiplication, addition and or subtraction of terms that results in the final results.
 
I have provided here an example for calculating the derivative of tan(x) from the first principles.