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Beliebt Rechnen >

derivative f(x)=(1+4x^2)(x-x^2)

Lösung

ableitung von

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

Lösung

- 16 x^{3} + 12 x^{2} - 2 x + 1

Schritte zur Lösung

\frac{d}{d x} ((1 + 4 x^{2}) (x - x^{2}))

Wende die Produktregel an:

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

f = 1 + 4 x^{2}, g = x - x^{2}

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

\frac{d}{d x} (1 + 4 x^{2}) = 8 x

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

= 8 x (x - x^{2}) + (1 - 2 x) (1 + 4 x^{2})

Vereinfache

8 x (x - x^{2}) + (1 - 2 x) (1 + 4 x^{2}) : - 16 x^{3} + 12 x^{2} - 2 x + 1

= - 16 x^{3} + 12 x^{2} - 2 x + 1

Graph

Beliebte Beispiele

tangent y=(1+2x)^9

t an g e n t y = (1 + 2 x)^{9}

derivative 2x^{1/2}

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(\partial)/(\partial y)(x^3-xy+y^3)

\frac{\partial}{\partial y} (x^{3} - x y + y^{3})

integral from 0 to 4 of x(4x-x^2)

\int_{0}^{4} x (4 x - x^{2}) d x

integral of 3/(9y^2-16)

\int \frac{3}{9 y ^{2} - 16} d y