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

Lösung

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

6 x (x^{2} + y^{2})^{2}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

= 3 (x^{2} + y^{2})^{2} \cdot 2 x

Vereinfache

= 6 x (x^{2} + y^{2})^{2}

\frac{\partial}{\partial x} (f (x, y) x (x, y))

\frac{d y}{d x} = 8 y

t an g e n t f (x) = (\frac{2}{x - 2}), at x = 4

\int_{0}^{l n (3)} \frac{3}{e ^{x} + 2} d x

(x - 2) \frac{d y}{d x} - y = 3