(\partial)/(\partial r)((x)(r+s))

Lösung

\frac{\partial}{\partial r} ((x) (r + s))

x

Schritte zur Lösung

\frac{\partial}{\partial r} ((x) (r + s))

Behandle

x, s

als Konstanten

Entferne die Konstante:

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

= x \frac{\partial}{\partial r} (r + s)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= x (\frac{\partial}{\partial r} (r) + \frac{\partial}{\partial r} (s))

\frac{\partial}{\partial r} (r) = 1

\frac{\partial}{\partial r} (s) = 0

= x (1 + 0)

Vereinfache

= x

e x p an d \frac{5 x + 2}{( x + 2 ) ( x + 1 )}

e x p an d x (x y^{2} + x^{2} = x + 3 y)

e x p an d \frac{2 y ^{2} - 2 x ^{2}}{( x ^{2} + y ^{2} ) ^{2}}

e x p an d \frac{4 - e ^{- t}}{( e ^{- t} + 1 ) ( e ^{- t} + 2 )}

\frac{\partial}{\partial y} ((x) (y^{4} + 3 y - 4 x^{3} - 5 x))