derivative of x^3e^{sqrt(x)}

Lösung

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

3 e^{x} x^{2} + \frac{e ^{x} x ^{\frac{5}{2}}}{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{3}, g = e^{x}

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

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

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

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

\frac{e ^{x}}{2 x} x^{3} = \frac{e ^{x} x ^{\frac{5}{2}}}{2}

= 3 e^{x} x^{2} + \frac{e ^{x} x ^{\frac{5}{2}}}{2}

\int \frac{1}{e ^{k x}} d x

y^{^{''}} + y = 0, y (0) = 0, y (π) = 0

t an g e n t y = 2 x + 1 (4.3)

\int x (x - 1)^{5} d x

\frac{\partial}{\partial x} (y^{\frac{1}{3}} x^{\frac{2}{3}})