(\partial)/(\partial x)(sin(nx)e^{-n^2t})

Lösung

\frac{\partial}{\partial x} (sin (n x) e^{- n^{2} t})

e^{- n^{2} t} cos (n x) n

Schritte zur Lösung

\frac{\partial}{\partial x} (sin (n x) e^{- n^{2} t})

Behandle

n, t

als Konstante

Entferne die Konstante:

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

= e^{- n^{2} t} \frac{\partial}{\partial x} (sin (n x))

Wende die Kettenregel an:

cos (n x) \frac{\partial}{\partial x} (n x)

= cos (n x) \frac{\partial}{\partial x} (n x)

\frac{\partial}{\partial x} (n x) = n

= e^{- n^{2} t} cos (n x) n

x \to \infty lim (1 - e^{x})

x \to - 1 lim (x^{2} + 4)

\int \frac{1}{5 + 2 x} d x

a re a y = \frac{5}{x}, y = \frac{5}{x ^{2}}, x = 6

x \to 0 lim (x^{x^{x}})