Tough times never last, but tough people do. – Dr. Robert Schuller

Derivative of following basic functions and constants using first principle

$$\sqrt{x}, x^n,$$ $$\frac{1}{x^n}, \log_e(x),$$ $$e^x, \sin (x), \cos (x),$$ $$\tan (x), \sec (x),$$ $$\cosec (x), \cot (x)$$