Find the derivation of each of the following from the first principle:
tan2x
Let f(x) = tan2x
We need to find the derivative of f(x) i.e. f’(x)
We know that,
…(i)
f(x) = tan2x
f(x + h) = tan2(x + h)
Putting values in (i), we get
Using:
[∵ sin A cos B – sin B cos A = sin(A – B)
& sin A cos B + sin B cos A = sin(A + B)]
Putting h = 0, we get
[∵ sin2x = 2sinxcosx]
= 2tanx sec2x
Hence, f’(x) = 2tanx sec2x