derivative of xsqrt(x^2+y^2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{2} + y^{2}

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

\int_{0}^{\frac{1}{5}} 5 arcsin (5 y) d y

f (x) = cos (5 x)

x \to - 1 lim (x + 2)

\frac{\partial}{\partial x} (18 x y)

x + y - 1 + (x - y + 3) y^{^{'}} = 0