The derivative of the function y tan x can be found using the product rule of differentiation.
If we let u = y and v = tan x, then the product rule states that the derivative of u v is given by:
(uv)’ = u’v + uv’
In this case, we first need to find the derivatives of u and v. Assuming y is a function of x, we have:
u’ = dy/dx
v’ = sec² x (the derivative of tan x).
Applying the product rule:
Derivative = (dy/dx) tan x + y sec² x
Thus, the derivative of y tan x is (dy/dx) tan x + y sec² x.