(\partial)/(\partial x)({f}(x)(x{f}(x)(x{f}(x))))

Lösung

\frac{\partial}{\partial x} (f (x) (x f (x) (x f (x))))

2 x f (x)^{3} + 3 f (x)^{2} \frac{\partial}{\partial x} (f (x)) x^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (f (x) (x f (x) (x f (x))))

Vereinfache

f (x) (x f (x) (x f (x))) : x^{2} f (x)^{3}

= \frac{\partial}{\partial x} (x^{2} f (x)^{3})

Wende die Produktregel an:

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

f = x^{2}, g = f (x)^{3}

= \frac{\partial}{\partial x} (x^{2}) f (x)^{3} + \frac{\partial}{\partial x} (f (x)^{3}) x^{2}

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

\frac{\partial}{\partial x} (f (x)^{3}) = 3 f (x)^{2} \frac{\partial}{\partial x} (f (x))

= 2 x f (x)^{3} + 3 f (x)^{2} \frac{\partial}{\partial x} (f (x)) x^{2}

\int e^{2 x} arcsin (e^{x}) d x

d er i v a t i v e (x^{3} + x)^{6}

\frac{\partial}{\partial y} (1 - x^{2} y)

\int \frac{x}{( 1 + x )} d x

\frac{d}{d x} ((4 x - 7)^{2})