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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

h

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

Beliebte Beispiele

derivative of 1/(sqrt(5x))

\frac{d}{d x} (\frac{1}{5 x})

integral of (sin(x)sqrt(x))/(sqrt(x))

\int \frac{sin ( x ) x}{x} d x

derivative (3x^2+3)(2x^2+1)

d er i v a t i v e (3 x^{2} + 3) (2 x^{2} + 1)

integral of-y/(x^2+y^2)

\int - \frac{y}{x ^{2} + y ^{2}} d x

limit as x approaches 2 of x^3-8

x \to 2 lim (x^{3} - 8)