(d^2}{d{x}d{y}}(({z})(e^{({x)/y)}ln({x}{y})-{z}))

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

e x p an d \frac{( s + 1 ) ( 1 + 50 s )}{25 ( s ^{2} + 150 s + 2 )}

e x p an d (2 x + 1) y^{'} (x)

e x p an d 4 (3 x^{2} - 2 x y - 5 y^{2})^{2}

e x p an d \frac{3}{2} sin (2 x) (3 cos (2 x) - 1)

e x p an d \frac{d}{d x} ((x + 6) \cdot e^{3 x}) + 4