What is the derivative of (1+9x^2(x-x^2)) ?

The derivative of (1+9x^2(x-x^2)) is -36x^3+27x^2-2x+1

What is the first derivative of (1+9x^2(x-x^2)) ?

The first derivative of (1+9x^2(x-x^2)) is -36x^3+27x^2-2x+1

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\frac{d}{d x} ((1 + 9 x^{2}) (x - x^{2}))

- 36 x^{3} + 27 x^{2} - 2 x + 1

Solution steps

\frac{d}{d x} ((1 + 9 x^{2}) (x - x^{2}))

Apply the Product Rule:

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

f = 1 + 9 x^{2}, g = x - x^{2}

= \frac{d}{d x} (1 + 9 x^{2}) (x - x^{2}) + \frac{d}{d x} (x - x^{2}) (1 + 9 x^{2})

\frac{d}{d x} (1 + 9 x^{2}) = 18 x

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

= 18 x (x - x^{2}) + (1 - 2 x) (1 + 9 x^{2})

Simplify

18 x (x - x^{2}) + (1 - 2 x) (1 + 9 x^{2}) : - 36 x^{3} + 27 x^{2} - 2 x + 1

= - 36 x^{3} + 27 x^{2} - 2 x + 1

\frac{d}{d x} (arctan (arcsin (x)))

\int 3 y^{5} y^{3} + 1 d y

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

\frac{d}{d x} (a x e^{- x})

\frac{\partial}{\partial x} (ln (a x + b y))

What is the derivative of (1+9x^2(x-x^2)) ?
The derivative of (1+9x^2(x-x^2)) is -36x^3+27x^2-2x+1
What is the first derivative of (1+9x^2(x-x^2)) ?
The first derivative of (1+9x^2(x-x^2)) is -36x^3+27x^2-2x+1