What is the derivative of f(x)=(1+6x^2)(x-x^2) ?

The derivative of f(x)=(1+6x^2)(x-x^2) is -24x^3+18x^2-2x+1

What is the first derivative of f(x)=(1+6x^2)(x-x^2) ?

The first derivative of f(x)=(1+6x^2)(x-x^2) is -24x^3+18x^2-2x+1

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derivative of

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

- 24 x^{3} + 18 x^{2} - 2 x + 1

Solution steps

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

Apply the Product Rule:

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

f = 1 + 6 x^{2}, g = x - x^{2}

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

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

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

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

Simplify

12 x (x - x^{2}) + (1 - 2 x) (1 + 6 x^{2}) : - 24 x^{3} + 18 x^{2} - 2 x + 1

= - 24 x^{3} + 18 x^{2} - 2 x + 1

n = 1 \sum \infty \frac{n x ^{n}}{n + 1}

\int_{0}^{2} (e^{x})^{2} d x

\int - x^{2} + 2 x d x

\frac{d}{d x} (\frac{x ^{6}}{3})

\int 6 x^{2} cos (2 x^{3} + 1) d x

What is the derivative of f(x)=(1+6x^2)(x-x^2) ?
The derivative of f(x)=(1+6x^2)(x-x^2) is -24x^3+18x^2-2x+1
What is the first derivative of f(x)=(1+6x^2)(x-x^2) ?
The first derivative of f(x)=(1+6x^2)(x-x^2) is -24x^3+18x^2-2x+1