derivative of x^6e^{5x}

Lösung

\frac{d}{d x} (x^{6} e^{5 x})

6 x^{5} e^{5 x} + e^{5 x} \cdot 5 x^{6}

Schritte zur Lösung

\frac{d}{d x} (x^{6} e^{5 x})

Wende die Produktregel an:

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

f = x^{6}, g = e^{5 x}

= \frac{d}{d x} (x^{6}) e^{5 x} + \frac{d}{d x} (e^{5 x}) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

= 6 x^{5} e^{5 x} + e^{5 x} \cdot 5 x^{6}

x \to 0 lim (\frac{( x ^{2} )}{x - 1})

t an g e n t y = \frac{1}{x ^{3}}, (2, \frac{1}{8})

\frac{d}{d x} (5 + 4 x)

\frac{\partial}{\partial y} (cos (2 x) sin (3 y))

25 y^{^{''}} - 40 y^{^{'}} + 16 y = 0, y (4) = 2, y^{^{'}} (4) = 2