(\partial)/(\partial x)(e^{x^2+y^2+z^2})

Lösung

\frac{\partial}{\partial x} (e^{x^{2} + y^{2} + z^{2}})

e^{x^{2} + y^{2} + z^{2}} \cdot 2 x

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{x^{2} + y^{2} + z^{2}})

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

e^{x^{2} + y^{2} + z^{2}} \frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2})

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

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

= e^{x^{2} + y^{2} + z^{2}} \cdot 2 x

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

\frac{\partial}{\partial y} (ln (x - 5 y))

a re a x^{2} + 4 x + 3, y = - 2, - 2 < x < 0

a re a x = y + 2, x = y^{2}

d er i v a t i v e \frac{1}{7 - 6 e ^{x}}