• Aplique a derivada
[tex]f'(x) = \frac{d}{dx} (x)[/tex]
• A derivada de uma variável elevada à 1 é sempre 1
[tex]f'(x) = \frac{d}{dx} (4)[/tex]
[tex]f'(x) = \frac{d}{dx} (2x)[/tex]
[tex]y' = \frac{d}{dx} ( {x}^{2} )[/tex]
[tex]y' = {2x}^{2 - 1} [/tex]
[tex]y' = {2x}^{1} [/tex]
[tex]y' = \frac{d}{dx} ( {3x}^{4} )[/tex]
[tex]y' = 3 \times \frac{d}{dx} ( {x}^{4} )[/tex]
[tex]y' = 3 \times {4x}^{4 - 1} [/tex]
[tex]y' = 3 \times {4x}^{3} [/tex]
[tex]y' = \frac{d}{dx} (6x + 18)[/tex]
[tex]y' = \frac{d}{dx} (6x) + \frac{d}{dx} (18)[/tex]
[tex]y' = 6 + 0[/tex]
[tex]f' (x) = \frac{d}{dx} ( {2x}^{2} - 8)[/tex]
[tex]f'(x) = \frac{d}{dx} ( {2x}^{2} ) - \frac{d}{dx} (8)[/tex]
[tex]f'(x) = 2 \times \frac{d}{dx} ( {x)}^{2} - \frac{d}{dx} (8)[/tex]
[tex]f'(x) = 2 \times 2x - \frac{d}{dx} (8)[/tex]
[tex]f'(x) = 2 \times 2x - 0[/tex]
[tex]f'(x) = \frac{d}{dx} ( {x}^{2} + 4x + 4)[/tex]
[tex]f'(x) = \frac{d}{dx} ( {x}^{2} ) + \frac{d}{dx} (4x) + \frac{d}{dx} (4)[/tex]
[tex]f'(x) = {2x}^{2 - 1} + 4 + 0 [/tex]
[tex]y' = \frac{d}{dx} (x + 1) \\ y' = \frac{d}{dx} (x) + \frac{d}{dx} (1) \\ y' = 1 + 0[/tex]
[tex]f'(x ) = \frac{d}{dx} ( {5x}^{4} - {4x}^{3} + {3x}^{2} - {2x}^{2} + 6x + 12)[/tex]
[tex]f'(x ) = \frac{d}{dx} ( {5x}^{4} - {4x}^{3} + {x}^{2} + 6x + 12)[/tex]
[tex]f'(x ) = \frac{d}{dx} ({5x}^{4}) - \frac{d}{dx}( {4x}^{3}) + \frac{d}{dx} ({x}^{2}) + \frac{d}{dx} (6x + 12)[/tex]
[tex]f'(x) = 5 \times \frac{d}{dx} ( {x}^{4} ) - 4 \times \frac{d}{dx} ( {x}^{3} ) + {2x}^{2 - 1} + 6 + 0[/tex]
[tex]f'(x) = 5 \times {4x}^{3} - 4 \times {3x}^{2} + 2x + 6[/tex]
[tex]{\huge\boxed { {\bf{E}}}\boxed { \red {\bf{a}}} \boxed { \blue {\bf{s}}} \boxed { \gray{\bf{y}}} \boxed { \red {\bf{}}} \boxed { \orange {\bf{M}}} \boxed {\bf{a}}}{\huge\boxed { {\bf{t}}}\boxed { \red {\bf{h}}}}[/tex]
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Lista de comentários
Derivadas
1) [tex]f(x) = x [/tex]
• Aplique a derivada
[tex]f'(x) = \frac{d}{dx} (x)[/tex]
• A derivada de uma variável elevada à 1 é sempre 1
Resposta: [tex]\color{green} \boxed{{ f'(x) = 1 }}[/tex]
2) [tex]f(x) = 4[/tex]
[tex]f'(x) = \frac{d}{dx} (4)[/tex]
Resposta: [tex]\color{green} \boxed{{ f'(x) = 0 }}[/tex]
3) [tex]f(x) = 2x[/tex]
[tex]f'(x) = \frac{d}{dx} (2x)[/tex]
Resposta: [tex]\color{green} \boxed{{f'(x) = 2 }}[/tex]
4) [tex]y = {x}^{2} [/tex]
[tex]y' = \frac{d}{dx} ( {x}^{2} )[/tex]
[tex]y' = {2x}^{2 - 1} [/tex]
[tex]y' = {2x}^{1} [/tex]
Resposta: [tex]\color{green} \boxed{{ y' = 2x }}[/tex]
5) [tex]y = {3x}^{4} [/tex]
[tex]y' = \frac{d}{dx} ( {3x}^{4} )[/tex]
[tex]y' = 3 \times \frac{d}{dx} ( {x}^{4} )[/tex]
[tex]y' = 3 \times {4x}^{4 - 1} [/tex]
[tex]y' = 3 \times {4x}^{3} [/tex]
Resposta: [tex]\color{green} \boxed{{y' = {12x}^{3} }}[/tex]
6) [tex]y = 6x + 18[/tex]
[tex]y' = \frac{d}{dx} (6x + 18)[/tex]
[tex]y' = \frac{d}{dx} (6x) + \frac{d}{dx} (18)[/tex]
[tex]y' = 6 + 0[/tex]
Resposta: [tex]\color{green} \boxed{{ y' = 6}}[/tex]
7) [tex]f(x) = {2x}^{2} - 8[/tex]
[tex]f' (x) = \frac{d}{dx} ( {2x}^{2} - 8)[/tex]
[tex]f'(x) = \frac{d}{dx} ( {2x}^{2} ) - \frac{d}{dx} (8)[/tex]
[tex]f'(x) = 2 \times \frac{d}{dx} ( {x)}^{2} - \frac{d}{dx} (8)[/tex]
[tex]f'(x) = 2 \times 2x - \frac{d}{dx} (8)[/tex]
[tex]f'(x) = 2 \times 2x - 0[/tex]
Resposta: [tex]\color{green} \boxed{{f '(x) = 4x }}[/tex]
8) [tex]f(x) = {x}^{2} + 4x + 4[/tex]
[tex]f'(x) = \frac{d}{dx} ( {x}^{2} + 4x + 4)[/tex]
[tex]f'(x) = \frac{d}{dx} ( {x}^{2} ) + \frac{d}{dx} (4x) + \frac{d}{dx} (4)[/tex]
[tex]f'(x) = {2x}^{2 - 1} + 4 + 0 [/tex]
Resposta: [tex]\color{green} \boxed{{f' (x) = 2x + 4 }}[/tex]
9) [tex]y = x + 1[/tex]
[tex]y' = \frac{d}{dx} (x + 1) \\ y' = \frac{d}{dx} (x) + \frac{d}{dx} (1) \\ y' = 1 + 0[/tex]
Resposta: [tex]\color{green} \boxed{{ y' = 1 }}[/tex]
10) [tex]f(x ) = {5x}^{4} - {4x}^{3} + {3x}^{2} - {2x}^{2} + 6x + 12[/tex]
[tex]f'(x ) = \frac{d}{dx} ( {5x}^{4} - {4x}^{3} + {3x}^{2} - {2x}^{2} + 6x + 12)[/tex]
[tex]f'(x ) = \frac{d}{dx} ( {5x}^{4} - {4x}^{3} + {x}^{2} + 6x + 12)[/tex]
[tex]f'(x ) = \frac{d}{dx} ({5x}^{4}) - \frac{d}{dx}( {4x}^{3}) + \frac{d}{dx} ({x}^{2}) + \frac{d}{dx} (6x + 12)[/tex]
[tex]f'(x) = 5 \times \frac{d}{dx} ( {x}^{4} ) - 4 \times \frac{d}{dx} ( {x}^{3} ) + {2x}^{2 - 1} + 6 + 0[/tex]
[tex]f'(x) = 5 \times {4x}^{3} - 4 \times {3x}^{2} + 2x + 6[/tex]
Resposta: [tex]\color{green} \boxed{{ f'(x) = 20 {x}^{3} - 12 {x}^{2} + 2x + 6 }}[/tex]
[tex]{\huge\boxed { {\bf{E}}}\boxed { \red {\bf{a}}} \boxed { \blue {\bf{s}}} \boxed { \gray{\bf{y}}} \boxed { \red {\bf{}}} \boxed { \orange {\bf{M}}} \boxed {\bf{a}}}{\huge\boxed { {\bf{t}}}\boxed { \red {\bf{h}}}}[/tex]