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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende Radikal Regel an:

a = a^{\frac{1}{2}}

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

Wende die Potenzregel an:

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

= 2 y^{2} \frac{1}{2} x^{\frac{1}{2} - 1}

Vereinfache

2 y^{2} \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{y ^{2}}{x}

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

\int e^{\frac{1}{x}} - e^{\frac{1}{x + 1}} d x

\frac{d}{d x} (ln (e^{x} - y))

\int x^{3} x^{2} - 1 d x

\frac{d}{d x} (\frac{1}{( x ^{2} - 1 ) ( x ^{2} + 3 x + 3 )})

\int sin^{3} (7 x) cos^{- 2} (7 x) d x