derivative f(x)=x^2(4x^3-1)

Lösung

ableitung von

f (x) = x^{2} (4 x^{3} - 1)

20 x^{4} - 2 x

Schritte zur Lösung

\frac{d}{d x} (x^{2} (4 x^{3} - 1))

Wende die Produktregel an:

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

f = x^{2}, g = 4 x^{3} - 1

= \frac{d}{d x} (x^{2}) (4 x^{3} - 1) + \frac{d}{d x} (4 x^{3} - 1) x^{2}

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

\frac{d}{d x} (4 x^{3} - 1) = 12 x^{2}

= 2 x (4 x^{3} - 1) + 12 x^{2} x^{2}

Vereinfache

2 x (4 x^{3} - 1) + 12 x^{2} x^{2} : 20 x^{4} - 2 x

= 20 x^{4} - 2 x

\int \frac{x ^{2} - 36}{x ^{4}} d x

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

t an g e n t 3 x^{2} + 2

d er i v a t i v e y = (x^{2} + 3 x) 2

\frac{\partial}{\partial x} (5 x^{2} + y^{2} + 9)