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Beliebt Rechnen >

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

Lösung

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

Lösung

- 2 e^{y^{2} - x^{2}} x

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

= e^{y^{2} - x^{2}} (- 2 x)

Vereinfache

= - 2 e^{y^{2} - x^{2}} x

Beliebte Beispiele

(1+x^2)(dy)/(dx)-2xy=0

(1 + x^{2}) \frac{d y}{d x} - 2 x y = 0

(dy)/(dx)=(3x+xy^2)/(2y+x^2y)

\frac{d y}{d x} = \frac{3 x + x y ^{2}}{2 y + x ^{2} y}

derivative of x(ln(5x)^2)

\frac{d}{d x} (x (ln (5 x))^{2})

y^'-3y=e^{3x}sqrt(4-x^2)

y^{^{'}} - 3 y = e^{3 x} 4 - x^{2}

limit as x approaches-2-of x+1

x \to - 2 - lim (x + 1)