What is the derivative of (2x^3+4x^2(4x^2+2x)) ?

The derivative of (2x^3+4x^2(4x^2+2x)) is 40x^4+80x^3+24x^2

What is the first derivative of (2x^3+4x^2(4x^2+2x)) ?

The first derivative of (2x^3+4x^2(4x^2+2x)) is 40x^4+80x^3+24x^2

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

40 x^{4} + 80 x^{3} + 24 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (2 x^{3} + 4 x^{2}) = 6 x^{2} + 8 x

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

= (6 x^{2} + 8 x) (4 x^{2} + 2 x) + (8 x + 2) (2 x^{3} + 4 x^{2})

Simplify

(6 x^{2} + 8 x) (4 x^{2} + 2 x) + (8 x + 2) (2 x^{3} + 4 x^{2}) : 40 x^{4} + 80 x^{3} + 24 x^{2}

= 40 x^{4} + 80 x^{3} + 24 x^{2}

What is the derivative of (2x^3+4x^2(4x^2+2x)) ?
The derivative of (2x^3+4x^2(4x^2+2x)) is 40x^4+80x^3+24x^2
What is the first derivative of (2x^3+4x^2(4x^2+2x)) ?
The first derivative of (2x^3+4x^2(4x^2+2x)) is 40x^4+80x^3+24x^2