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Iff(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+...

`Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4),` then find the value of `f^(prime)(2)`

Text Solution

Verified by Experts

The correct Answer is:
`2//17`
`g(x)=int_(2)^(x)(tdt)/(1+t^(4))` or `g'(x)=x/(1+x^(4))` or `g'(2)=2/17`
Now `f(x)=e^(g(x))` or `f'(x)=e^(g(x))g'(x)` or `f'(2)=e^(g(2))g'(2)`
`:.f'(2)=e^(0)xx2/17=2/17` as `g(2)=0`
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