Tag: differentiation by substitution

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Multiple choice maths differencial calculus - differenciability and methods of differnciation differentiation by substitution methods of differentiation derivative of a function

If $f(x) =x^{3} + e^{x/2}$ then $g"(1)$ is equal to, (where $f(x)$ and $g(x)$ are inverse functions of each other).

  1. $2$
  2. $-2$
  3. $-\dfrac {1}{2}$
  4. $\dfrac {1}{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$g(f(x))=x$
$g'f(x)=1/f'(X)$
$g''f(x)=\dfrac{f''(x)}{{f'(x)}^3}$
$f(x)=1 at x=0$
$f(0)=1$
$f'(x)=3x^2+e^{(x/2)}/2$
$f'(0)=1/2$
$f''(x)=6x+e^{x/2}/4$
$f''(0)=1/4$
$g''(1)=\dfrac{-1/4}{1/8}=-2$