What is the second derivative of f(x)= sec^2x?

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##f''(x)=4tan^2xsec^2x+2sec^4x##

To furnish the primary derivative, we succeed bear to use the on the assist government.

Use the government 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 furnish the assist derivative, we succeed bear to use the .

##f''(x)=2tanxd/dx(sec^2x)+2sec^2xd/dx(tanx)##

Note that we already comprehend 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##

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