Find the derivation of each of the following from the first principle:

Question

Find the derivation of each of the following from the first principle: tan (3x + 1)

Philoid · Accepted Answer

Let f(x) = tan (3x + 1)

We need to find the derivative of f(x) i.e. f’(x)

We know that,

…(i)

f(x) = tan (3x + 1)

f(x + h) = tan [3(x + h) + 1]

Putting values in (i), we get

Using the formula:

Putting h = 0, we get

= 3sec²(3x+ 1)

Hence, f’(x) = 3sec²(3x+ 1)