Question

differentiate y=5tan(nx) where n is a positive integer. i know the derivative of 5tan(x) would be 5(sec(x))^2 but i dont know how the n fits in.

Answer 1

use chain rule.

Answer 2

erg
\[y'= 5n*sec^2(nx)\]

Answer 3

ohh i see, thanks

Answer 4

5 is a constant multiple, so you leave it alone. The derivative of tan(nx) = sec^2(nx), but then you have to multiply with the derivative of the inside which is derivative of nx. Since n is a number the derivative of nx = x.

Answer 5

derivative of nx = n ... not x. sorry

Answer 6

if it is the case of 5tanx then you can do the same, but now derivative of x = 1, so you don't include 1 most of the time.