derivative of {f}(x(x{f}(x)(x{f}(x))))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

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

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

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

\frac{d}{d x} (3^{x l n (x)})

d er i v a t i v e lo g_{e} (sin (2 x) + cot (2 x))

d er i v a t i v e y = \frac{1}{2} x

\int_{π}^{2 π} (t - π) e^{- s t} d t

d er i v a t i v e 13 - x^{2}