(\partial)/(\partial x)((x+y)^2+(x+1)^2)

Lösung

\frac{\partial}{\partial x} ((x + y)^{2} + (x + 1)^{2})

4 x + 2 y + 2

Schritte zur Lösung

\frac{\partial}{\partial x} ((x + y)^{2} + (x + 1)^{2})

Vereinfache

(x + y)^{2} + (x + 1)^{2} : 2 x^{2} + 2 x y + 2 x + y^{2} + 1

= \frac{\partial}{\partial x} (2 x^{2} + 2 x y + 2 x + y^{2} + 1)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (2 x^{2}) + \frac{\partial}{\partial x} (2 x y) + \frac{\partial}{\partial x} (2 x) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (2 x^{2}) = 4 x

\frac{\partial}{\partial x} (2 x y) = 2 y

\frac{\partial}{\partial x} (2 x) = 2

\frac{\partial}{\partial x} (y^{2}) = 0

\frac{\partial}{\partial x} (1) = 0

= 4 x + 2 y + 2 + 0 + 0

Vereinfache

= 4 x + 2 y + 2

\int \frac{1}{2} sin^{2} (x) d x

\frac{\partial}{\partial x} (x + y^{2})

in v erse l a pl a ce \frac{3}{s ^{2} + 6 s + 10}

d er i v a t i v e 2 cos^{3} (t)

\int e^{\frac{1}{3} x} d x