What is the derivative of #sec(x-x^2)#?
If you are studying maths, then you should learn the Chain Rule for Differentiation, and practice how to use it:
# y=f(x) #then # f'(x)=dy/dx=dy/(du)(du)/dx #
I was taught to remember that the differential can be treated like a fraction and that the "
# dy/dx = dy/(dv)(dv)/(du)(du)/dx #etc, or # (dy/dx = dy/color(red)cancel(dv)color(red)cancel(dv)/color(blue)cancel(du)color(blue)cancel(du)/dx) #
(NB you should know that
# dy/dx = secutanu(1-2x) #
# dy/dx = (1-2x) sec(x-x^2)tan(x-x^2)#
you start of with:
The derivative of sec(x) is sex(x)tan(x) because:
USELESS UNLESS YOU WANT TO KNOW HOW TO GET THE DERIVATIVE SEC(X) IF YOU FORGOT THE FORMULA:
since we have
the derivative of cos(x) is -sin(x), and the derivative of 1 is 0:
Continuing on with the previous discussion
sec(x) is sex(x)tan(x), so:
The derivative of