(\partial)/(\partial α)({K}(α)(α)^αL^{1-α})

Soluzione

\frac{\partial}{\partial α} (K (α) (α)^{α} L^{1 - α})

\frac{\partial}{\partial α} (K (α)) α^{α} L^{1 - α} + (L^{1 - α} α^{α} (ln (α) + 1) - L^{1 - α} α^{α} ln (L)) K (α)

Fasi della soluzione

\frac{\partial}{\partial α} (K (α) (α)^{α} L^{1 - α})

Applica la regola del prodotto:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = K (α), g = α^{α} L^{1 - α}

= \frac{\partial}{\partial α} (K (α)) α^{α} L^{1 - α} + \frac{\partial}{\partial α} (α^{α} L^{1 - α}) K (α)

\frac{\partial}{\partial α} (α^{α} L^{1 - α}) = L^{1 - α} α^{α} (ln (α) + 1) - L^{1 - α} α^{α} ln (L)

= \frac{\partial}{\partial α} (K (α)) α^{α} L^{1 - α} + (L^{1 - α} α^{α} (ln (α) + 1) - L^{1 - α} α^{α} ln (L)) K (α)

t an g e n t y = 11 x^{2}, (- 2, 44)

x \to 1 lim (\frac{3 x}{x ^{2} - 1})

t a y l or e^{- 5 x}

\int_{1}^{9} \frac{1}{2 x} d x

\frac{d}{d x} (7 (2 x e^{x} + e^{x} x^{2}))