(\partial)/(\partial x)(7sqrt(x^2+y^2))

Lösung

\frac{\partial}{\partial x} (7 x^{2} + y^{2})

\frac{7 x}{x ^{2} + y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (7 x^{2} + y^{2})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 7 \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

= 7 \cdot \frac{1}{2 x ^{2} + y ^{2}} \cdot 2 x

Vereinfache

7 \cdot \frac{1}{2 x ^{2} + y ^{2}} \cdot 2 x : \frac{7 x}{x ^{2} + y ^{2}}

= \frac{7 x}{x ^{2} + y ^{2}}

t an g e n t f (x) = x^{4} - 5 x^{2} + 2, at x = 2

\frac{d}{d x} (5 (e^{x} cos (x) - e^{x} sin (x)))

\int x 6 - x d x

x \to 3 lim (\frac{x - 1}{x ^{2} - 1})

in v erse l a pl a ce e^{- 2 s} \frac{1}{s - 9}