Question

If f(x) = then f '(1) =

• A. 1
• B. 2
• C. 3
• D. None

Answer 1

Answer: (D)

None

Answer 2

f'(x)= $\left| \begin{matrix} 0 & 0 & 0 \\ x & x^{2} & x^{3} \\ e^{x–a} & e^{x^{2}–a^{2}} & e^{x^{3}–a^{3}} \end{matrix} \right|$ +

$\left| \begin{matrix} 1 & 2a & 3a^{2} \\ 1 & 2x & 3x^{2} \\ e^{x–a} & e^{x^{2}–a^{2}} & e^{x^{3}–a^{3}} \end{matrix} \right|$ + $\left| \begin{matrix} 1 & 2a & 3a^{2} \\ x & x^{2} & x^{3} \\ e^{x–a} & 2xe^{x^{2}–a^{2}} & 3x^{2}e^{x^{3}–a^{3}} \end{matrix} \right|$

Ž f '(1) = 0 + 0 + 0 = 0