(\partial)/(\partial x)(x^2+2xy+3y^4)

Lösung

\frac{\partial}{\partial x} (x^{2} + 2 x y + 3 y^{4})

2 x + 2 y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} + 2 x y + 3 y^{4})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (2 x y) + \frac{\partial}{\partial x} (3 y^{4})

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

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

\frac{\partial}{\partial x} (3 y^{4}) = 0

= 2 x + 2 y + 0

Vereinfache

= 2 x + 2 y

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

d er i v a t i v e y = ln (\frac{4}{x ^{3}})

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

\frac{\partial}{\partial x} (e^{(x - y)})

\frac{\partial}{\partial x} (x + y cos (y))