(\partial)/(\partial x)(e^{xy}+1/(x+y))

Lösung

\frac{\partial}{\partial x} (e^{x y} + \frac{1}{x + y})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{x y} + \frac{1}{x + y})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

t an g e n t 4 x^{2} + 2 x - 1

f (x) = (5 x^{6} + 4 x^{3})^{4}

\frac{\partial}{\partial x} (ln (8 x + 7 y))

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y = x e^{x}

\int_{1}^{5} \frac{x}{x ^{2} + 6 x + 13} d x