Differentiate each of the following from first principle: `tan(2x+1)`

Options

A. 2 sec(2x+1)
B. `sec^2(2x+1)`
C. `2sec^2(2x+1)`
D. `2cos^2(2x+1)`

Explanation

We have,
f(x) = tan (2x+1)



`f'(x)= lim_(h->0)(f(x+h)-f(x))/h`



`=lim_(h->0)(tan {2(x+h)+1}-tan (2x+1))/h`



`=f'(x)= lim_(h->0)1/h*(sin(2x+2h +1-2x-1))/(cos {2(x+h)+1} cos(2x+1)`
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