Let be a function such that for all Then
Explanation of correct answer :
Determining the value of :
We have,
Differentiating the equation:
Differentiating equation ,
Differentiating equation ,
Substituting we get,
Substituting in equation in .
Substituting in equation .
Now substituting the value of in equation .
Now, substituting the value of in equation
Now, putting the values of in .
Hence, the value of is .
Therefore, the correct answer is option (C).