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

Lösung

ableitung von

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

f (4 x^{3} + 6 x^{2})

Schritte zur Lösung

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

Behandle

f

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

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

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

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

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

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

Multipliziere aus

2 x (x^{2} + 2 x) + (2 x + 2) x^{2} : 4 x^{3} + 6 x^{2}

= f (4 x^{3} + 6 x^{2})

\frac{\partial}{\partial y} (3 x cos (y))

\int \frac{21}{x ( x ^{2} + 4 ) ^{2}} d x

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

x \to 1 + lim (\frac{1}{1 - x ^{2}})

d er i v a t i v e f (x) = x e^{x^{2}}