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Beliebt Rechnen >

derivative of {g}(h,x(h(x)))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

h

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

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

Beliebte Beispiele

integral from 0 to 2 of xe^{4x}

\int_{0}^{2} x e^{4 x} d x

y^{^{'}} = y^{3}, y (0) = 1

(dy)/(dt)+1/2 y=17sin(2t)

\frac{d y}{d t} + \frac{1}{2} y = 17 sin (2 t)

integral of cos(sqrt(2x))

\int cos (2 x) d x

integral of (tan(x))^4

\int (tan (x))^{4} d x