derivative 6x^2*e^{(x^3)/3}

Lösung

ableitung von

6 x^{2} \cdot e^{\frac{x ^{3}}{3}}

6 (2 e^{\frac{x ^{3}}{3}} x + e^{\frac{x ^{3}}{3}} x^{4})

Schritte zur Lösung

\frac{d}{d x} (6 x^{2} e^{\frac{x ^{3}}{3}})

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{2}, g = e^{\frac{x ^{3}}{3}}

= 6 (\frac{d}{d x} (x^{2}) e^{\frac{x ^{3}}{3}} + \frac{d}{d x} (e^{\frac{x ^{3}}{3}}) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (e^{\frac{x ^{3}}{3}}) = e^{\frac{x ^{3}}{3}} x^{2}

= 6 (2 x e^{\frac{x ^{3}}{3}} + e^{\frac{x ^{3}}{3}} x^{2} x^{2})

e^{\frac{x ^{3}}{3}} x^{2} x^{2} = e^{\frac{x ^{3}}{3}} x^{4}

= 6 (2 e^{\frac{x ^{3}}{3}} x + e^{\frac{x ^{3}}{3}} x^{4})

d er i v a t i v e 8 x + 9 x

l a pl a ce t r an s f or m (1 + t)^{7}

\int \frac{x ^{2}}{( x + 1 ) ^{2}} d x

\int_{1}^{6} x^{3} ln (4 x) d x

in v erse l a pl a ce \frac{( s + 1 )}{( s + 2 ) ^{2}}