(d^2)/(dx^2)((z)(x^2+y^2+z^2-c^2))

Lösung

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

x^{2} \frac{d ^{2} z}{d x ^{2}} + 4 x \frac{d z}{d x} - c^{2} \frac{d ^{2} z}{d x ^{2}} + 2 z + 4 y \frac{d z}{d x} \frac{d y}{d x} + y^{2} \frac{d ^{2} z}{d x ^{2}} + 6 z \frac{d z}{d x}^{2} + 3 z^{2} \frac{d ^{2} z}{d x ^{2}} + 2 z \frac{d y}{d x}^{2} + 2 zy \frac{d ^{2} y}{d x ^{2}}

Schritte zur Lösung

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

\frac{d}{d x} (z (x^{2} + y^{2} + z^{2} - c^{2})) = x^{2} \frac{d z}{d x} + 2 x z - c^{2} \frac{d z}{d x} + y^{2} \frac{d z}{d x} + 3 z^{2} \frac{d z}{d x} + 2 zy \frac{d y}{d x}

= \frac{d}{d x} (x^{2} \frac{d z}{d x} + 2 x z - c^{2} \frac{d z}{d x} + y^{2} \frac{d z}{d x} + 3 z^{2} \frac{d z}{d x} + 2 zy \frac{d y}{d x})

\frac{d}{d x} (x^{2} \frac{d z}{d x} + 2 x z - c^{2} \frac{d z}{d x} + y^{2} \frac{d z}{d x} + 3 z^{2} \frac{d z}{d x} + 2 zy \frac{d y}{d x}) = x^{2} \frac{d ^{2} z}{d x ^{2}} + 4 x \frac{d z}{d x} - c^{2} \frac{d ^{2} z}{d x ^{2}} + 2 z + 4 y \frac{d z}{d x} \frac{d y}{d x} + y^{2} \frac{d ^{2} z}{d x ^{2}} + 6 z \frac{d z}{d x}^{2} + 3 z^{2} \frac{d ^{2} z}{d x ^{2}} + 2 z \frac{d y}{d x}^{2} + 2 zy \frac{d ^{2} y}{d x ^{2}}

= x^{2} \frac{d ^{2} z}{d x ^{2}} + 4 x \frac{d z}{d x} - c^{2} \frac{d ^{2} z}{d x ^{2}} + 2 z + 4 y \frac{d z}{d x} \frac{d y}{d x} + y^{2} \frac{d ^{2} z}{d x ^{2}} + 6 z \frac{d z}{d x}^{2} + 3 z^{2} \frac{d ^{2} z}{d x ^{2}} + 2 z \frac{d y}{d x}^{2} + 2 zy \frac{d ^{2} y}{d x ^{2}}

e x p an d \frac{10 - 4 s ^{2} - 11 s}{s ( s ^{2} - 2 s + 1 )}

e x p an d \frac{( 2 - x ) ( ln ( 1 - x ) )}{x}

e x p an d e^{y} (\frac{d y}{d x} + 1) =!

e x p an d \frac{( x - 2 ) ( 2 x + 3 )}{x + 47}

e x p an d 5 - 3 \cdot 2