Question

If f(x) = e^{log (x2 + 4x - 6)}, then what is the derivative of f(x)?
1. x² + 4
2. 2x² + 4
3. 2x + 4
4. x + 4

Answer 1

Correct Answer - Option 3 : 2x + 4

Concept used:

If y = e^logx then y = x

\(\rm d(x^n)\over{dx} \) = nx^{n - 1} 

Calculations:

Given, f(x) = e4log (x² + 4x - 6)

So, f(x) = x² + 4x - 6              (∵ elog x = x)

Taking derivative with respect to x on both side, we get 

f'(x) = 2x + 4