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

Lösung

ableitung von

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

4 x^{3} + 2 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

= 2 x (x^{2} + 1) + 2 x x^{2}

Vereinfache

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

= 4 x^{3} + 2 x

\frac{\partial}{\partial y} (x e^{- x^{2} - y^{2}})

\int_{0}^{4} x 16 - x^{2} d x

\int \frac{1 - t}{t} d t

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = - 3

\frac{d}{d x} (3 sin^{2} (2 x))