What is the second derivative of #f(x)=tan(3x)#?

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Answer 1 · 2015-12-14T06:48:42

#f''(x)=18sec^2(3x)tan(3x)#

We will use the chain rule, together with the derivatives:

First Derivative:
#f'(x) = d/dx tan(3x)#

#= sec^2(3x)(d/dx3x)#

#= 3sec^2(3x)#

Second Derivative:

#f''(x) = d/dx(f'(x))#

#= d/dx(3sec^2(3x))#

#= 3d/dx(sec^2(3x))#

#= 3(2sec(3x))(d/dxsec(3x))#

#=6sec(3x)(sec(3x)tan(3x))(d/dx3x)#

#=18sec^2(3x)tan(3x)#