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

The derivative of 2x^2(x-4x^3) is 2(-20x^4+3x^2)

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

The first derivative of 2x^2(x-4x^3) is 2(-20x^4+3x^2)

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

2 (- 20 x^{4} + 3 x^{2})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (x - 4 x^{3}) = 1 - 12 x^{2}

= 2 (2 x (x - 4 x^{3}) + (1 - 12 x^{2}) x^{2})

Expand

2 x (x - 4 x^{3}) + (1 - 12 x^{2}) x^{2} : - 20 x^{4} + 3 x^{2}

= 2 (- 20 x^{4} + 3 x^{2})

n = 0 \sum \infty 2 (- \frac{2}{3})

\frac{d x}{d t} + t^{3} x^{5} + \frac{x}{t} = 0

\int x^{2} ln (x + 4) d x

\frac{d}{d x} (e^{3 x} cos (x) + e^{3 x} sin (x))

\int x^{3} e^{- x^{2}} d x

What is the derivative of 2x^2(x-4x^3) ?
The derivative of 2x^2(x-4x^3) is 2(-20x^4+3x^2)
What is the first derivative of 2x^2(x-4x^3) ?
The first derivative of 2x^2(x-4x^3) is 2(-20x^4+3x^2)