(\partial)/(\partial x)(sqrt(2x^2+5y^2))

Lösung

\frac{\partial}{\partial x} (2 x^{2} + 5 y^{2})

\frac{2 x}{2 x ^{2} + 5 y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x^{2} + 5 y^{2})

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 2 x ^{2} + 5 y ^{2}} \frac{\partial}{\partial x} (2 x^{2} + 5 y^{2})

= \frac{1}{2 2 x ^{2} + 5 y ^{2}} \frac{\partial}{\partial x} (2 x^{2} + 5 y^{2})

\frac{\partial}{\partial x} (2 x^{2} + 5 y^{2}) = 4 x

= \frac{1}{2 2 x ^{2} + 5 y ^{2}} \cdot 4 x

Vereinfache

\frac{1}{2 2 x ^{2} + 5 y ^{2}} \cdot 4 x : \frac{2 x}{2 x ^{2} + 5 y ^{2}}

= \frac{2 x}{2 x ^{2} + 5 y ^{2}}

t an g e n t y = 2 x^{3} - 2 x (- 1)

\frac{d}{d x} (2 cos (- 2 x))

\int \frac{34 x ^{2}}{( 2 x + 1 ) ( x ^{2} + 4 )} d x

y^{^{'}} = - 3 x y^{3}

\int (6 x y) d x