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Beliebt Rechnen >

(\partial)/(\partial s)(3sqrt(s^2+t^2))

Lösung

\frac{\partial}{\partial s} (3 s^{2} + t^{2})

Lösung

\frac{3 s}{s ^{2} + t ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial s} (3 s^{2} + t^{2})

Behandle

t

als Konstante

Entferne die Konstante:

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

= 3 \frac{\partial}{\partial s} (s^{2} + t^{2})

Wende die Kettenregel an:

\frac{1}{2 s ^{2} + t ^{2}} \frac{\partial}{\partial s} (s^{2} + t^{2})

= \frac{1}{2 s ^{2} + t ^{2}} \frac{\partial}{\partial s} (s^{2} + t^{2})

\frac{\partial}{\partial s} (s^{2} + t^{2}) = 2 s

= 3 \cdot \frac{1}{2 s ^{2} + t ^{2}} \cdot 2 s

Vereinfache

3 \cdot \frac{1}{2 s ^{2} + t ^{2}} \cdot 2 s : \frac{3 s}{s ^{2} + t ^{2}}

= \frac{3 s}{s ^{2} + t ^{2}}

Beliebte Beispiele

domäne f(x)=(x^4+1)^7

d o main f (x) = (x^{4} + 1)^{7}

(dy)/(dx)=x-y,y(0)=2

\frac{d y}{d x} = x - y, y (0) = 2

limit as x approaches 0 of ln(1/(x^2))

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

(\partial)/(\partial z)(y^2z)

\frac{\partial}{\partial z} (y^{2} z)

integral from 0 to N of e^{-st}cos(3t)

\int_{0}^{N} e^{- s t} cos (3 t) d t