Matematică >> funcţii derivabile >> 1
exemple
De exemplu:
1. Derivata funcției \( f : D \rightarrow \mathbb{R} \), \( f(x) = 5x^4 -7x^2 -8x +9 \).
\( f(x) = 5x^4 -7x^2 -8x +9 \)
\( f(x) = 5x^{\color{red}4} -7x^{\color{red}2} -8x^{\color{blue}1} +\color{darkmagenta}9 \)
\( f'(x) = 5 \cdot \color{red}4 \color{dimgray} x^{\color{red}4-1} -7 \cdot \color{red}2 \color{dimgray} x^{\color{red}2-1} -8x^{\color{blue}1-1} +\color{darkmagenta}0 \)
\( f'(x) = 20x^3 -14x -8 \).
1. Derivata funcției \( f : D \rightarrow \mathbb{R} \), \( f(x) = 5x^4 -7x^2 -8x +9 \).
\( f(x) = 5x^4 -7x^2 -8x +9 \)
\( f(x) = 5x^{\color{red}4} -7x^{\color{red}2} -8x^{\color{blue}1} +\color{darkmagenta}9 \)
\( f'(x) = 5 \cdot \color{red}4 \color{dimgray} x^{\color{red}4-1} -7 \cdot \color{red}2 \color{dimgray} x^{\color{red}2-1} -8x^{\color{blue}1-1} +\color{darkmagenta}0 \)
\( f'(x) = 20x^3 -14x -8 \).
exerciții
exercițiu nou
Derivata funcţiei \( f : D \rightarrow \mathbb{R} \),
\(f(x)=6x^{3}-2x^{2}+5x+3\)
este:
exercițiu nou
Derivata funcţiei \( f : D \rightarrow \mathbb{R} \),
\(f(x)=6x^{3}-2x^{2}+5x+3\)
este:
\(f'(x)=\)\(18x^{2}-4x+5\).
Avem:
\(f(x) = 6x^{3}-2x^{2}+5x+3\)
\(f(x) = 6x^{ \color{red}3 \color{dimgray}}-2x^{ \color{red}2 \color{dimgray}}+5x^{ \color{blue}1 \color{dimgray}} \color{darkmagenta}+3 \color{dimgray}\)
\(f'(x) = 6\cdot \color{red}3 \color{dimgray}x^{ \color{red}3-1 \color{dimgray}}-2\cdot \color{red}2 \color{dimgray}x^{ \color{red}2-1 \color{dimgray}}+5x^{ \color{blue}1-1 \color{dimgray}} \color{darkmagenta}+0 \color{dimgray}\)
\(f'(x) = \)\(18x^{2}-4x+5\).