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Question: If f(x) = \(\left| \begin{matrix} 1 & 2a & 3a^{2} \\ x & x^{2} & x^{3} \\ e^{x–a} & e^{x^{2}–a^{2}} ...

If f(x) = ∣12a3a2xx2x3ex–aex2–a2ex3–a3∣\left| \begin{matrix} 1 & 2a & 3a^{2} \\ x & x^{2} & x^{3} \\ e^{x–a} & e^{x^{2}–a^{2}} & e^{x^{3}–a^{3}} \end{matrix} \right| then f '(1) =

A

1

B

2

C

3

D

None

Answer

None

Explanation

Solution

f '(x)= ∣000xx2x3ex–aex2–a2ex3–a3∣\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|+∣12a3a212x3x2ex–aex2–a2ex3–a3∣\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|

+ ∣12a3a2xx2x3ex–a2xex2–a23x2ex3–a3∣\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