What is the second derivative of ##f(x)= sec^2x##?
February 20th, 2023
##f”(x)=4tan^2xsec^2x+2sec^4x##
To find the first derivative, we will have to use the on the second power.
Use the rule that ##d/dx(u^2)=2u*u’##.
Thus, we see that
##f'(x)=2secx*d/dx(secx)##
##f'(x)=2secx*secxtanx##
##f'(x)=2sec^2xtanx##
To find the second derivative, we will have to use the .
##f”(x)=2tanxd/dx(sec^2x)+2sec^2xd/dx(tanx)##
Note that we already know that ##d/dx(sec^2x)=2sec^2xtanx## and that ##d/dx(tanx)=sec^2x##.
This gives us
##f”(x)=2tanx(2sec^2xtanx)+2sec^2x(sec^2x)##
##f”(x)=4tan^2xsec^2x+2sec^4x##