If #f(x) =tan^2(x/2) # and #g(x) = sqrt(5x-1 #, what is #f'(g(x)) #?

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Answer 1 · 2016-03-16T13:05:20

#f'(g(x))=tan(sqrt(5x-1)/2)xxsec^2(sqrt(5x-1)/2)#

As #f(x)=tan^2(x/2)#,

#f'(x)=(d(tan^2(x/2)))/(d(tanx/2))##xx##(d(tanx/2))/(d(x/2))##xx##(d(x/2))/dx#

Hence #f'(x)=2tan(x/2)xxsec^2(x/2)xx1/2#

or #f'(x)=tan(x/2)xxsec^2(x/2)#

Hence #f'(g(x))=tan(g(x)/2)xxsec^2(g(x)/2)#

and as #g(x)=sqrt(5x-1)#

#f'(g(x))=tan(sqrt(5x-1)/2)xxsec^2(sqrt(5x-1)/2)#