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 \( f : D \rightarrow \mathbb{R} \),
\(f(x)=-6x^{8}+5x^{6}-2x^{5}+9x^{2}+7x\)

este:

 \( f'(x) = \) \(-48x^{7}+30x^{5}-10x^{4}+18x+7\)
 \( f'(x) = \) \(-6x^{7}+5x^{5}-2x^{4}+9x+7\)
 \( f'(x) = \) \(-48x^{8}+30x^{6}-10x^{5}+18x^{2}+7x\)
 \( f'(x) = \) \(2x^{7}+11x^{5}+3x^{4}+11x+8\)
 \( f'(x) = \) \(-48x^{8}+30x^{6}-10x^{5}+18x^{2}\)


 


exercițiu nou

Derivata funcţiei \( f : D \rightarrow \mathbb{R} \),
\(f(x)=-6x^{8}+5x^{6}-2x^{5}+9x^{2}+7x\)
este:

\(f'(x)=\)\(-48x^{7}+30x^{5}-10x^{4}+18x+7\).

Avem:
\(f(x) = -6x^{8}+5x^{6}-2x^{5}+9x^{2}+7x\)
\(f(x) = -6x^{ \color{red}8 \color{dimgray}}+5x^{ \color{red}6 \color{dimgray}}-2x^{ \color{red}5 \color{dimgray}}+9x^{ \color{red}2 \color{dimgray}}+7x^{ \color{blue}1 \color{dimgray}}\)
\(f'(x) = -6\cdot \color{red}8 \color{dimgray}x^{ \color{red}8-1 \color{dimgray}}+5\cdot \color{red}6 \color{dimgray}x^{ \color{red}6-1 \color{dimgray}}-2\cdot \color{red}5 \color{dimgray}x^{ \color{red}5-1 \color{dimgray}}+9\cdot \color{red}2 \color{dimgray}x^{ \color{red}2-1 \color{dimgray}}+7x^{ \color{blue}1-1 \color{dimgray}}\)
\(f'(x) = \)\(-48x^{7}+30x^{5}-10x^{4}+18x+7\).