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Popular Precálculo >

derivative y=2x^2(3x-4)

Solución

derivada de

y = 2 x^{2} (3 x - 4)

Solución

2 (9 x^{2} - 8 x)

Pasos de solución

\frac{d}{d x} (2 x^{2} (3 x - 4))

Sacar la constante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (x^{2} (3 x - 4))

Aplicar la regla del producto:

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

f = x^{2}, g = 3 x - 4

= 2 (\frac{d}{d x} (x^{2}) (3 x - 4) + \frac{d}{d x} (3 x - 4) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (3 x - 4) = 3

= 2 (2 x (3 x - 4) + 3 x^{2})

Expandir

2 x (3 x - 4) + 3 x^{2} : 9 x^{2} - 8 x

= 2 (9 x^{2} - 8 x)

Gráfica

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