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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d y}{d x} = \frac{y ^{2} - 1}{x ^{2} - 1}, y (5) = 5

\frac{d}{d x} ((3 x - 2)^{5})

\int 4 e^{x} 8 + e^{x} d x

x \to 6 lim (x + 3)

(arctan (e^{x}))^{^{'}}