A) \[\sec \,\,x\]
B) \[\sec \,\,(g\,\,(x))\]
C) \[\cos \,(g\,(x))\]
D) \[-\sin \,\,(g\,(x)\,)\]
Correct Answer: B
Solution :
Given, \[g(x)\] is the inverse of \[f(x)\] and \[f'(x)=cos\,\,x\] ?.(i) \[\Rightarrow \] \[g(x)={{f}^{-1}}(x)\] \[\Rightarrow \] \[x=f(g(x))\] On differentiating \[\Rightarrow \] \[1=f'\,(g(x)).g'(x)\] \[\Rightarrow \]\[g'(x)=\frac{1}{f'(g(x))}=\frac{1}{\cos \,(g(x))}\][from Eq.(i)] \[\Rightarrow \] \[g'(x)=sec\,g\,(x)\]
You need to login to perform this action.
You will be redirected in
3 sec
