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Question : 151 of 180
Marks:
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Solution:
‌‌ We have, ‌f(x)=logx2(log‌x)‌⇒‌‌f(x)=‌[logx(log‌x)]‌‌[∵loganb=‌logab]‌⇒‌‌f(x)=‌[‌]‌‌(∵logab=‌)‌f′(x)=‌[‌| log(x)‌[log(log(x))]−log(log‌x)‌‌log‌x |
| (log‌x)2 |
]‌=‌[‌| log(x)‌×−(log(log‌x)‌) |
| (log‌x)2 |
]‌=‌[‌]‌⇒‌‌f′(x)=‌[‌| 1−log‌log(x) |
| x(log‌x)2 |
]‌⇒‌‌f′(e)=‌[‌| 1−log‌log(e) |
| e(log‌e)2 |
]=‌[‌]=‌
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