Turunan (SIMAK UI 11 – Kode 315)

Jika g(x) = (f\circ f\circ f)(x) dengan f(0)=0 dan f'(0)=2, maka g'(x) = ...
  1.   0
  2.   2
  3.   4
  4.   8
  5.   16

 
Jawab :
Dari sifat komposisi fungsi dan aturan rantai untuk turunan …
\displaystyle \begin{aligned} g(x) &= f\Big(f\big(f(x)\big)\Big) \\ g'(x) &= f'\Big(f\big(f(x)\big)\Big)\cdot f'\big(f(x)\big)\cdot f'(x) \\ g'(0) &= f'\Big(f\big(f(0)\big)\Big)\cdot f'\big(f(0)\big)\cdot f'(0) \\ g'(0) &= f'\big(f(0)\big)\cdot f'(0)\cdot 2 \\ g'(0) &= f'(0)\cdot 2\cdot 2 \\ g'(0) &= 8 \end{aligned}
Jawaban : D
catatan :
Aturan rantai
\boxed{~h(x) = f\big(g(x)\big) \rightarrow h'(x) = f'\big(g(x)\big)\cdot g'(x)~}
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