derivative of e^{x^{3+6x^2}}

Lösung

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

e^{x^{3 + 6 x^{2}}} x^{3 + 6 x^{2}} (12 x ln (x) + \frac{3 + 6 x ^{2}}{x})

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x^{3 + 6 x^{2}}) = x^{3 + 6 x^{2}} (12 x ln (x) + \frac{3 + 6 x ^{2}}{x})

= e^{x^{3 + 6 x^{2}}} x^{3 + 6 x^{2}} (12 x ln (x) + \frac{3 + 6 x ^{2}}{x})

\frac{d y}{d t} = \frac{y}{1 + t} - \frac{y}{t} + t^{2} (1 + t)

\frac{\partial}{\partial x} ((13 x - 1) (3 y - 1))

d er i v a t i v e y = ln (3 x - 7)

\int \frac{2 x ^{3} - x ^{2} + 2 x + 2}{x ^{2} + 1} d x

t a y l or \frac{1}{x - 1}, 10