d/(dy)(xy+ysqrt(x^2+y^2))

Lösung

\frac{d}{d y} (x y + y x^{2} + y^{2})

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

Schritte zur Lösung

\frac{d}{d y} (x y + y x^{2} + y^{2})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d y} (x y) = x

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

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

\frac{d}{d x} (2190 \cdot e^{- 0.3 x})

x \to \frac{π}{2} + lim (3 e^{t a n (x)})

\frac{d}{d x} (sin (x^{2}) + \frac{( 1 - x )}{1 + x})

\int 15 sin^{3} (x co) s^{2} x d x

\frac{\partial}{\partial x} (x + y - 3)