(\partial)/(\partial x)(sqrt(x^2+y^2)+1)

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (1) = 0

= \frac{x}{x ^{2} + y ^{2}} + 0

Vereinfache

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

d er i v a t i v e f (x) = \frac{x}{( x - 7 ) ^{2}}

f (x) = \frac{( e ^{x} + e ^{- x} )}{2}

x \to 0 lim (\frac{x}{x + ∣ x ∣})

a re a y = \frac{1}{18 x ^{2}}, y = x, y = \frac{x}{10}

\int \frac{x - 4}{x ^{2}} d x