What is the derivative of (4x^2+4(2x^2+2x)) ?

The derivative of (4x^2+4(2x^2+2x)) is 32x^3+24x^2+16x+8

What is the first derivative of (4x^2+4(2x^2+2x)) ?

The first derivative of (4x^2+4(2x^2+2x)) is 32x^3+24x^2+16x+8

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

32 x^{3} + 24 x^{2} + 16 x + 8

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (4 x^{2} + 4) = 8 x

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

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

Simplify

8 x (2 x^{2} + 2 x) + (4 x + 2) (4 x^{2} + 4) : 32 x^{3} + 24 x^{2} + 16 x + 8

= 32 x^{3} + 24 x^{2} + 16 x + 8

\frac{d}{d x} (3^{2 x^{2}} \cdot x)

\frac{d}{d x} (\frac{10}{x ^{2} + 1})

x \to - 4 lim (\frac{1}{2} x - 1)

\frac{7 e ^{x} x ^{\frac{5}{2}}}{2} + e^{x} x^{\frac{7}{2}}

\int 0.4 \cdot e^{- 2000 x} d x

What is the derivative of (4x^2+4(2x^2+2x)) ?
The derivative of (4x^2+4(2x^2+2x)) is 32x^3+24x^2+16x+8
What is the first derivative of (4x^2+4(2x^2+2x)) ?
The first derivative of (4x^2+4(2x^2+2x)) is 32x^3+24x^2+16x+8