derivative of (y^2+x^2e^{y^2-x^2})

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y^{2} + x^{2}, g = e^{y^{2} - x^{2}}

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

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

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

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

\frac{d}{d x} (- 20 x^{3} + 12 x^{2} - 20)

\frac{d}{d x} (arctan (\frac{5 x}{4}))

\frac{d}{d x} (e^{x} (x + 6))

x \to - 9 lim (\frac{9 - ∣ x ∣}{9 + x})

\int e^{- x} sin (w x) d x