A) \[1+{{x}^{5}}\]
B) \[5{{x}^{4}}\]
C) \[\frac{1}{1+{{(g(x))}^{5}}}\]
D) \[1+{{(g(x))}^{5}}\]
Correct Answer: D
Solution :
| We have,\[f'(x)=\frac{1}{1+{{x}^{5}}}\] |
| \[g(x)\] is universe of \[f(x)\]. |
| \[\therefore \,\,\,\,\,\,\,\,\,f(g(x))=x\] |
| On differentiating, we get |
| \[f'(g(x).g'(x))=1\]\[\Rightarrow \,\,\,g'\left( x \right)=\frac{1}{f'(gx)}\]\[\Rightarrow \,\,\,g'\left( x \right)=\frac{1}{\frac{1}{1+(g{{(x)}^{5}})}}\]\[\Rightarrow \,\,\,g'\left( x \right)=1+(g{{(x)}^{5}})\] |
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