Question

Limit of (tan3(x+h) - tan3x)/h where h is approaching 0

Answer 1

Answer: 3sec²(3x)

Explanation:

The definition of derivative is:

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

From the given problem, we can see that tan3(x+h) is f(x+h) and tan3x is f(x).

Since we now know what f(x) is, we can find f'(x), or the limit of (tan3(x+h) - tan3x)/h where h is approaching 0.

f(x) = tan3x

f'(x) = sec²(3x) * 3

f'(x) = 3sec²(3x)