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Beliebt Rechnen >

derivative of ax^2(x-3+bx^4(ln(x/3)))

Lösung

\frac{d}{d x} (a x^{2} (x - 3) + b x^{4} (ln (\frac{x}{3})))

Lösung

a (3 x^{2} - 6 x) + b (4 x^{3} ln (\frac{x}{3}) + x^{3})

Schritte zur Lösung

\frac{d}{d x} (a x^{2} (x - 3) + b x^{4} (ln (\frac{x}{3})))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (a x^{2} (x - 3)) + \frac{d}{d x} (b x^{4} ln (\frac{x}{3}))

\frac{d}{d x} (a x^{2} (x - 3)) = a (3 x^{2} - 6 x)

\frac{d}{d x} (b x^{4} ln (\frac{x}{3})) = b (4 x^{3} ln (\frac{x}{3}) + x^{3})

= a (3 x^{2} - 6 x) + b (4 x^{3} ln (\frac{x}{3}) + x^{3})

Graph

Beliebte Beispiele

integral of (2t)/(1-t^2)

\int \frac{2 t}{1 - t ^{2}} d t

sum from n=1 to infinity of n*2^{-n}

n = 1 \sum \infty n \cdot 2^{- n}

-5t^2y^{''}-2ty^'+14y=0

- 5 t^{2} y^{^{''}} - 2 t y^{^{'}} + 14 y = 0

derivative x^2e^x-2xe^x+5e^x

d er i v a t i v e x^{2} e^{x} - 2 x e^{x} + 5 e^{x}

limit as x approaches 0 of (x^2+5x)/x

x \to 0 lim (\frac{x ^{2} + 5 x}{x})