(\partial)/(\partial x)((e^v)/(u(v,x)+v^2))

Lösung

\frac{\partial}{\partial x} (\frac{e ^{v}}{u ( v , x ) + v ^{2}})

e^{v} (- \frac{1}{( u ( v , x ) + v ^{2} ) ^{2}} (\frac{\partial}{\partial x} (u (v, x)) + 0))

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{e ^{v}}{u ( v , x ) + v ^{2}})

Behandle

v

als Konstante

Entferne die Konstante:

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

= e^{v} \frac{\partial}{\partial x} (\frac{1}{u ( v , x ) + v ^{2}})

Wende Exponentenregel an:

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

= e^{v} \frac{\partial}{\partial x} ((u (v, x) + v^{2})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( u ( v , x ) + v ^{2} ) ^{2}} \frac{\partial}{\partial x} (u (v, x) + v^{2})

= - \frac{1}{( u ( v , x ) + v ^{2} ) ^{2}} \frac{\partial}{\partial x} (u (v, x) + v^{2})

\frac{\partial}{\partial x} (u (v, x) + v^{2}) = \frac{\partial}{\partial x} (u (v, x)) + 0

= e^{v} (- \frac{1}{( u ( v , x ) + v ^{2} ) ^{2}} (\frac{\partial}{\partial x} (u (v, x)) + 0))

(e^{x})^{^{'}}

d er i v a t i v e f (x) = x^{5} + \frac{1}{x ^{5}}

\int \frac{2}{x ^{3}} + \frac{3}{x ^{2}} + 5 d x

x^{^{''}} + x^{^{'}} = 0

d er i v a t i v e x^{2} arctan (5 x)