Question

Alguém por favor me ajuda ???

Answer 1

Derivadas

1) $f(x) = x$

• Aplique a derivada

$f'(x) = \frac{d}{dx} (x)$

• A derivada de uma variável elevada à 1 é sempre 1

Resposta: $\color{green} \boxed{{ f'(x) = 1 }}$

2) $f(x) = 4$

$f'(x) = \frac{d}{dx} (4)$

Resposta: $\color{green} \boxed{{ f'(x) = 0 }}$

3) $f(x) = 2x$

$f'(x) = \frac{d}{dx} (2x)$

Resposta: $\color{green} \boxed{{f'(x) = 2 }}$

4) $y = {x}^{2}$

$y' = \frac{d}{dx} ( {x}^{2} )$

$y' = {2x}^{2 - 1}$

$y' = {2x}^{1}$

Resposta: $\color{green} \boxed{{ y' = 2x }}$

5) $y = {3x}^{4}$

$y' = \frac{d}{dx} ( {3x}^{4} )$

$y' = 3 \times \frac{d}{dx} ( {x}^{4} )$

$y' = 3 \times {4x}^{4 - 1}$

$y' = 3 \times {4x}^{3}$

Resposta: $\color{green} \boxed{{y' = {12x}^{3}   }}$

6) $y = 6x + 18$

$y' = \frac{d}{dx} (6x + 18)$

$y' = \frac{d}{dx} (6x) + \frac{d}{dx} (18)$

$y' = 6 + 0$

Resposta: $\color{green} \boxed{{ y' = 6}}$

7) $f(x) = {2x}^{2} - 8$

$f' (x) = \frac{d}{dx} ( {2x}^{2} - 8)$

$f'(x) = \frac{d}{dx} ( {2x}^{2} ) - \frac{d}{dx} (8)$

$f'(x) = 2 \times \frac{d}{dx} ( {x)}^{2} - \frac{d}{dx} (8)$

$f'(x) = 2 \times 2x - \frac{d}{dx} (8)$

$f'(x) = 2 \times 2x - 0$

Resposta: $\color{green} \boxed{{f '(x) = 4x }}$

8) $f(x) = {x}^{2} + 4x + 4$

$f'(x) = \frac{d}{dx} ( {x}^{2} + 4x + 4)$

$f'(x) = \frac{d}{dx} ( {x}^{2} ) + \frac{d}{dx} (4x) + \frac{d}{dx} (4)$

$f'(x) = {2x}^{2 - 1} + 4 + 0$

Resposta: $\color{green} \boxed{{f' (x) = 2x + 4 }}$

9) $y = x + 1$

$y' = \frac{d}{dx} (x + 1) \\ y' = \frac{d}{dx} (x) + \frac{d}{dx} (1) \\ y' = 1 + 0$

Resposta: $\color{green} \boxed{{ y' = 1 }}$

10) $f(x ) = {5x}^{4} - {4x}^{3} + {3x}^{2} - {2x}^{2} + 6x + 12$

$f'(x ) = \frac{d}{dx} ( {5x}^{4} - {4x}^{3} + {3x}^{2} - {2x}^{2} + 6x + 12)$

$f'(x ) = \frac{d}{dx} ( {5x}^{4} - {4x}^{3} + {x}^{2} + 6x + 12)$

$f'(x ) = \frac{d}{dx} ({5x}^{4}) - \frac{d}{dx}( {4x}^{3}) + \frac{d}{dx} ({x}^{2}) + \frac{d}{dx} (6x + 12)$

$f'(x) = 5 \times \frac{d}{dx} ( {x}^{4} ) - 4 \times \frac{d}{dx} ( {x}^{3} ) + {2x}^{2 - 1} + 6 + 0$

$f'(x) = 5 \times {4x}^{3} - 4 \times {3x}^{2} + 2x + 6$

Resposta: $\color{green} \boxed{{ f'(x) = 20 {x}^{3} - 12 {x}^{2} + 2x + 6 }}$

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