Question

Como calcular a derivada de f(x)=3x^2-6x+8

Answer 1

Resposta:

f'(x) = 6x - 6

Explicação passo a passo:

f(x) = 3x² - 6x + 8

Regra da soma / subtração:

f'(x) = (3x²)' - (6x)' + (8)'

Regra da Potência: → (Lembrando que derivada de constante vale 0).

f'(x) = 3(2x²⁻¹) - 6(1x¹⁻¹) + 0

f'(x) = 3(2x¹) - 6(1x⁰)

f'(x) = 3(2x) - 6(1(1))

f'(x) = 6x - 6(1)

f'(x) = 6x - 6

Answer 2

$\Large\mathsf\displaystyle{}f\left(x\right) = {3x}^{2} - 6x + 8 \\\\ \Large\mathsf\displaystyle{} {f}^{'} = \dfrac{d}{dx} \left( {3x}^{2} - 6x + 8 \right) \\ \\ \Large\mathsf\displaystyle{} {f}^{'} = \dfrac{d}{dx} \left( {3x}^{2} \right) + \dfrac{d}{dx} \left( - 6x\right) + \dfrac{d}{dx} \left(8\right) \\ \\\Large\mathsf\displaystyle{} {f}^{'} = 3\cdot2x + \dfrac{d}{dx} \left( - 6x\right) + \dfrac{d}{dx} \left(8\right) \\\\ \Large\mathsf\displaystyle{} {f}^{'} = 3\cdot2x - 6x + \dfrac{d}{dx} \left(8\right) \\ \\ \Large\mathsf\displaystyle{} {f}^{'} = 3\cdot2x - 6 + 0 \\ \\\LARGE\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{ {f}^{'} = 6x - 6 }}}\end{gathered} }$

$\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{{ \red{Bons}} \blue{\:Estudos}}}}\end{gathered} }$