I am trying to find:
dy/dx for y = sec(tan x)
I have the answer, but I have no idea how to get there. I know that the derivative of sec x = sec x tan x and that the derivative of tan x is sec^2 x. But sec doesn't have an x, so ...?
d/dx secu = secu tanu du/dx, so
y' = sec(tanx) tan(tanx) sec^2(x)
thanks!!!!!!
To find the derivative of y = sec(tan x), we need to use the chain rule. The chain rule states that if we have a function f(g(x)), the derivative of f(g(x)) with respect to x is given by f'(g(x)) * g'(x).
Let's break down the steps:
1. First, identify the composite function. In this case, we have y = sec(tan x), where the outer function is sec(x) and the inner function is tan(x).
2. Find the derivative of the outer function: The derivative of sec(x) is sec(x) * tan(x). As you already mentioned, the derivative of sec(x) is sec(x) * tan(x).
3. Find the derivative of the inner function: The derivative of tan(x) is sec^2(x). As you mentioned, the derivative of tan(x) is sec^2(x).
4. Now, apply the chain rule: Multiply the derivative of the outer function by the derivative of the inner function.
dy/dx = (sec(tan x))' = sec(x) * tan(x) * sec^2(x)
So, the derivative of y = sec(tan x) is dy/dx = sec(x) * tan(x) * sec^2(x).
This can also be simplified further:
dy/dx = sec(x) * tan(x) * sec^2(x) = sec^3(x) * tan(x)