What is (\partial)/(\partial x)((x-2)(x^2+4)) ?

The answer to (\partial)/(\partial x)((x-2)(x^2+4)) is 3x^2-4x+4

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(\partial)/(\partial x)((x-2)(x^2+4))

\frac{\partial}{\partial x} ((x - 2) (x^{2} + 4))

3 x^{2} - 4 x + 4

Solution steps

\frac{\partial}{\partial x} ((x - 2) (x^{2} + 4))

Apply the Product Rule:

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

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

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

\frac{\partial}{\partial x} (x - 2) = 1

\frac{\partial}{\partial x} (x^{2} + 4) = 2 x

= 1 \cdot (x^{2} + 4) + 2 x (x - 2)

Simplify

1 \cdot (x^{2} + 4) + 2 x (x - 2) : 3 x^{2} - 4 x + 4

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

x v^{'} + v = - \frac{4 - v + v ^{2}}{1 - v + 4 v ^{2}}

\int \frac{64 + x ^{2}}{x} d x

h \to 0 lim (\frac{( 3 ^{h} - 1 )}{h})

y^{^{'}} = 8 + t - y

3^{s i n (x)}

What is (\partial)/(\partial x)((x-2)(x^2+4)) ?
The answer to (\partial)/(\partial x)((x-2)(x^2+4)) is 3x^2-4x+4