derivative (1+7x^2)(x-x^2)

Lösung

ableitung von

(1 + 7 x^{2}) (x - x^{2})

- 28 x^{3} + 21 x^{2} - 2 x + 1

Schritte zur Lösung

\frac{d}{d x} ((1 + 7 x^{2}) (x - x^{2}))

Wende die Produktregel an:

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

f = 1 + 7 x^{2}, g = x - x^{2}

= \frac{d}{d x} (1 + 7 x^{2}) (x - x^{2}) + \frac{d}{d x} (x - x^{2}) (1 + 7 x^{2})

\frac{d}{d x} (1 + 7 x^{2}) = 14 x

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

= 14 x (x - x^{2}) + (1 - 2 x) (1 + 7 x^{2})

Vereinfache

14 x (x - x^{2}) + (1 - 2 x) (1 + 7 x^{2}) : - 28 x^{3} + 21 x^{2} - 2 x + 1

= - 28 x^{3} + 21 x^{2} - 2 x + 1

\int_{0}^{\frac{π}{4}} tan^{2} (x) d x

\int \frac{3 x ^{2}}{125} d x

d er i v a t i v e sin (cos (tan (x)))

\frac{d}{d x} (1 + cos (2 x))

d er i v a t i v e y = 5 x^{4}