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

Lösung

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

\frac{2 x}{2 x ^{2} + 2 y ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

= \frac{1}{2 2 x ^{2} + 2 y ^{2}} \cdot 4 x

Vereinfache

\frac{1}{2 2 x ^{2} + 2 y ^{2}} \cdot 4 x : \frac{2 x}{2 x ^{2} + 2 y ^{2}}

= \frac{2 x}{2 x ^{2} + 2 y ^{2}}

l a pl a ce t r an s f or m z

\int \frac{12}{3 x + x x} d x

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

d er i v a t i v e f (x) = ln (2)

\int 3 e^{4} d x