(\partial)/(\partial x)(x^2(1-y^{2/5}))

Lösung

\frac{\partial}{\partial x} (x^{2} (1 - y^{\frac{2}{5}}))

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

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} (1 - y^{\frac{2}{5}}))

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Vereinfache

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

d er i v a t i v e y = x + x^{\frac{3}{2}} - 8 x

(5 x^{3} + 3 x y + 2 y^{2}) d x + (x^{2} + 2 x y) d y = 0

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

x \to 0 lim (ln (2 x^{2} + x))

\int \frac{x}{x ^{2} + 49} d x