Categories > differentiation > Differentiation by substitution > If ${{f}_{n}}(x)$, ${{g}_{n}}(x)$, ${{h}_{n}}(x),n=1,\,2,\,3$are polynomials in x such that ${{f}_{n}}(a)={{g}_{n}}(a)={{h}_{n}}(a),n=1,2,3$ and $F(x) = \begin{vmatrix} {{f_1}(x)}&{{f_2}(x)}&{{f_3}(x)}\\ {{g_1}(x)}&{{g_2}(x)}&{{g_3}(x)}\\ {{h_1}(x)}&{{h_2}(x)}&{{h_3}(x)} \end{vmatrix}$. Then ${F}'(a)$is equal to

differentiation

Question: If ${{f}_{n}}(x)$, ${{g}_{n}}(x)$, ${{h}_{n}}(x),n=1,\,2,\,3$are polynomials in x such that ${{f}_{n}}(a)={{g}_{n}}(a)={{h}_{n}}(a),n=1,2,3$ and $F(x) = \begin{vmatrix} {{f_1}(x)}&{{f_2}(x)}&{{f_3}(x)}\\ {{g_1}(x)}&{{g_2}(x)}&{{g_3}(x)}\\ {{h_1}(x)}&{{h_2}(x)}&{{h_3}(x)} \end{vmatrix}$. Then ${F}'(a)$is equal to


1) 0
2) ${{f}_{1}}(a){{g}_{2}}(a){{h}_{3}}(a)$
3) 1
4) None of these
Solution: Explanation: No Explanation
Differentiation by substitution Higher order derivatives

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