derivative of f(h,x(g(h,x)(h(x))))

Lösung

\frac{d}{d x} (f (h, x) (g (h, x) (h (x))))

h (\frac{d}{d x} (f (h, x)) g (h, x) x + (\frac{d}{d x} (g (h, x)) x + 1 \cdot g (h, x)) f (h, x))

Schritte zur Lösung

\frac{d}{d x} (f (h, x) (g (h, x) (h (x))))

Behandle

h

als Konstante

Entferne die Konstante:

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

= h \frac{d}{d x} (f (h, x) g (h, x) x)

Wende die Produktregel an:

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

f = f (h, x), g = g (h, x) x

= h (\frac{d}{d x} (f (h, x)) g (h, x) x + \frac{d}{d x} (g (h, x) x) f (h, x))

\frac{d}{d x} (g (h, x) x) = \frac{d}{d x} (g (h, x)) x + 1 \cdot g (h, x)

= h (\frac{d}{d x} (f (h, x)) g (h, x) x + (\frac{d}{d x} (g (h, x)) x + 1 \cdot g (h, x)) f (h, x))

d er i v a t i v e (x + 1)^{2}

\frac{d y}{d x} = \frac{x ^{3} + 2 y ^{3}}{x y ^{2}}

in v erse l a pl a ce e^{- π s} \frac{2}{s ^{3}}

d er i v a t i v e 2 x csc (x) - x^{2} cot (x) csc (x)

\int_{3}^{\infty} e^{- \frac{x}{4}} d x