What is the derivative of (x^3-2x(-x+6x^2)) ?

The derivative of (x^3-2x(-x+6x^2)) is 30x^4-4x^3-36x^2+4x

What is the first derivative of (x^3-2x(-x+6x^2)) ?

The first derivative of (x^3-2x(-x+6x^2)) is 30x^4-4x^3-36x^2+4x

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\frac{d}{d x} ((x^{3} - 2 x) (- x + 6 x^{2}))

30 x^{4} - 4 x^{3} - 36 x^{2} + 4 x

Solution steps

\frac{d}{d x} ((x^{3} - 2 x) (- x + 6 x^{2}))

Apply the Product Rule:

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

f = x^{3} - 2 x, g = - x + 6 x^{2}

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

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

\frac{d}{d x} (- x + 6 x^{2}) = - 1 + 12 x

= (3 x^{2} - 2) (- x + 6 x^{2}) + (- 1 + 12 x) (x^{3} - 2 x)

Simplify

(3 x^{2} - 2) (- x + 6 x^{2}) + (- 1 + 12 x) (x^{3} - 2 x) : 30 x^{4} - 4 x^{3} - 36 x^{2} + 4 x

= 30 x^{4} - 4 x^{3} - 36 x^{2} + 4 x

(e^{2 x} + 9) \frac{d y}{d x} = y

\int (x^{2} + 2 x + 1) d x

f (x) = (- 25 x^{2} + 1)^{2}

\int \frac{1}{3} cos (3 x) d x

(y^{3} - 1) e^{x} d x + 3 y^{2} (e^{x} + 1) d y = 0, y (0) = 0

What is the derivative of (x^3-2x(-x+6x^2)) ?
The derivative of (x^3-2x(-x+6x^2)) is 30x^4-4x^3-36x^2+4x
What is the first derivative of (x^3-2x(-x+6x^2)) ?
The first derivative of (x^3-2x(-x+6x^2)) is 30x^4-4x^3-36x^2+4x