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Beliebt Rechnen >

(\partial)/(\partial x)((x^2+y^2)^6)

Lösung

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{6})

Lösung

12 x (x^{2} + y^{2})^{5}

Schritte zur Lösung

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{6})

Behandle

y

als Konstante

Wende die Kettenregel an:

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

= 6 (x^{2} + y^{2})^{5} \frac{\partial}{\partial x} (x^{2} + y^{2})

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

= 6 (x^{2} + y^{2})^{5} \cdot 2 x

Vereinfache

= 12 x (x^{2} + y^{2})^{5}

Beliebte Beispiele

limit as x approaches 5 of 3

x \to 5 lim (3)

(xdy)/(dx)-y=3x^4

\frac{x d y}{d x} - y = 3 x^{4}

y^{''}-6y^'+25y=e^t

y^{^{''}} - 6 y^{^{'}} + 25 y = e^{t}

integral of x^3arctan(x)

\int x^{3} arctan (x) d x

d/(dθ)(θsin(θ))

\frac{d}{d θ} (θ sin (θ))