Funcții derivabile

Exerciții și probleme... funcții derivabile.

Matematică >> funcţii derivabile >> 1


teorie


exemple
De exemplu:

1. Derivata funcției \( f : D \rightarrow \mathbb{R} \), \( f(x) = 5x^4 -7x^2 -8x +9 \).

\( f(x) = 5x^4 -7x^2 -8x +9 \)
\( f(x) = 5x^{\color{red}4} -7x^{\color{red}2} -8x^{\color{blue}1} +\color{darkmagenta}9 \)
\( f'(x) = 5 \cdot \color{red}4 \color{dimgray} x^{\color{red}4-1} -7 \cdot \color{red}2 \color{dimgray} x^{\color{red}2-1} -8x^{\color{blue}1-1} +\color{darkmagenta}0 \)
\( f'(x) = 20x^3 -14x -8 \).

exerciții

Derivata funcţiei \( f : D \rightarrow \mathbb{R} \),
\(f(x)=5x^{7}-x^{5}+5x^{2}-3x+7\)

este:

 \( f'(x) = \) \(35x^{6}-5x^{4}+10x+7\)
 \( f'(x) = \) \(35x^{7}-5x^{5}+10x^{2}\)
 \( f'(x) = \) \(35x^{6}-5x^{4}+10x-3\)
 \( f'(x) = \) \(35x^{7}-5x^{5}+10x^{2}-3x+7\)
 \( f'(x) = \) \(5x^{6}-x^{4}+5x-3\)


 


exercițiu nou

Derivata funcţiei \( f : D \rightarrow \mathbb{R} \),
\(f(x)=5x^{7}-x^{5}+5x^{2}-3x+7\)
este:

\(f'(x)=\)\(35x^{6}-5x^{4}+10x-3\).

Avem:
\(f(x) = 5x^{7}-x^{5}+5x^{2}-3x+7\)
\(f(x) = 5x^{ \color{red}7 \color{dimgray}}-x^{ \color{red}5 \color{dimgray}}+5x^{ \color{red}2 \color{dimgray}}-3x^{ \color{blue}1 \color{dimgray}} \color{darkmagenta}+7 \color{dimgray}\)
\(f'(x) = 5\cdot \color{red}7 \color{dimgray}x^{ \color{red}7-1 \color{dimgray}}-1\cdot \color{red}5 \color{dimgray}x^{ \color{red}5-1 \color{dimgray}}+5\cdot \color{red}2 \color{dimgray}x^{ \color{red}2-1 \color{dimgray}}-3x^{ \color{blue}1-1 \color{dimgray}} \color{darkmagenta}+0 \color{dimgray}\)
\(f'(x) = \)\(35x^{6}-5x^{4}+10x-3\).