The derivative of f(tanx) with respect to g(secx) at x=π4, where f'(1)=2 and g'(2)=4, is
12
2
1
None of these
Explanation for the correct option:
Finding the derivative of f(tanx) with respect to g(secx):
Let
υ=ftanx,v=gsecxddxu=dudx=ddxftanx=dftanxdtanxxdtanxdxChainRule=f'tanxxsec2x=f'tanxsec2x
Now,
ddxv=dvdx=ddxgsecx=dgsecxdsecxxdsecxdxChainRule=g'secxxsecxtanx
dudv=dudxdvdx=f'tanxsec2xg'secxsecxtanx=f'tanxsecxg'secxtanx
Giventhatx=π4dudv=f'tanπ4secπ4g'secπ4tanπ4=f'12g'21=2241=22=22×2=12
Therefore, the correct answer is option (A).