d/(dt)((x)(2sinh(t)+3t^2))

Lösung

\frac{d}{d t} ((x) (2 sinh (t) + 3 t^{2}))

\frac{d x}{d t} (2 sinh (t) + 3 t^{2}) + (2 cosh (t) + 6 t) x

Schritte zur Lösung

\frac{d}{d t} ((x) (2 sinh (t) + 3 t^{2}))

Wende die Produktregel an:

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

f = x, g = 2 sinh (t) + 3 t^{2}

= \frac{d x}{d t} (2 sinh (t) + 3 t^{2}) + \frac{d}{d t} (2 sinh (t) + 3 t^{2}) x

\frac{d}{d t} (2 sinh (t) + 3 t^{2}) = 2 cosh (t) + 6 t

= \frac{d x}{d t} (2 sinh (t) + 3 t^{2}) + (2 cosh (t) + 6 t) x

e x p an d \frac{( x ^{n + 1} - ( n + 1 ) x + n )}{x - 1}

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e x p an d (3 x y^{2} + 3 x^{2}) d x + (2 x^{2} y + 4 y^{3}) d x