Cho hàm số \[y = \sin \left( {{e^{f\left( x \right)}}} \right)\]. Tính y’
A.
\[f'\left( x \right){e^{f\left( x \right)}}\cos \left( {f\left( x \right)} \right)\]
B.
\[f'\left( x \right){e^{f\left( x \right)}}\cos \left( {{e^{f\left( x \right)}}} \right)\]
C.
\[{e^{f\left( x \right)}}\cos \left( {{e^{f\left( x \right)}}} \right)\]
D.
\[ - f'\left( x \right){e^{f\left( x \right)}}\cos \left( {{e^{f\left( x \right)}}} \right)\]
Trả lời:
Đáp án đúng: B
Ta có: \[
\begin{array}{l}
y = \sin \left( {{e^{f\left( x \right)}}} \right)\\
y' = {\left[ {\sin \left( {{e^{f\left( x \right)}}} \right)} \right]^'}\\
= \cos \left( {{e^{f\left( x \right)}}} \right).{\left( {{e^{f\left( x \right)}}} \right)^'}\\
= \cos \left( {{e^{f\left( x \right)}}} \right).{e^{f\left( x \right)}}.f'\left( x \right)\\
= f'\left( x \right){e^{f\left( x \right)}}\cos \left( {{e^{f\left( x \right)}}} \right)
\end{array}
\]
Vậy đáp án đúng là B.