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))

\int \frac{cos ( 2 x )}{cos ( x ) - sin ( x )} d x

\frac{d}{d x} (5 cos^{- 4} (x))

\int \frac{e ^{2 x}}{e ^{2 x} - 1} d x

\frac{d}{d x} (sin (x + π))

ma c l a u r in x^{2} e^{x}