(d^2)/(dx^2)((y)(4x^2+3y^2))

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (4 x^{2} + 3 y^{2}))

4 x^{2} \frac{d ^{2} y}{d x ^{2}} + 16 x \frac{d y}{d x} + 8 y + 18 y \frac{d y}{d x}^{2} + 9 y^{2} \frac{d ^{2} y}{d x ^{2}}

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (4 x^{2} + 3 y^{2}))

\frac{d}{d x} (y (4 x^{2} + 3 y^{2})) = 4 x^{2} \frac{d y}{d x} + 8 x y + 9 y^{2} \frac{d y}{d x}

= \frac{d}{d x} (4 x^{2} \frac{d y}{d x} + 8 x y + 9 y^{2} \frac{d y}{d x})

\frac{d}{d x} (4 x^{2} \frac{d y}{d x} + 8 x y + 9 y^{2} \frac{d y}{d x}) = 4 x^{2} \frac{d ^{2} y}{d x ^{2}} + 16 x \frac{d y}{d x} + 8 y + 18 y \frac{d y}{d x}^{2} + 9 y^{2} \frac{d ^{2} y}{d x ^{2}}

= 4 x^{2} \frac{d ^{2} y}{d x ^{2}} + 16 x \frac{d y}{d x} + 8 y + 18 y \frac{d y}{d x}^{2} + 9 y^{2} \frac{d ^{2} y}{d x ^{2}}

e x p an d \frac{π ( e ^{2} - 1 )}{2}

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

e x p an d \frac{( x + 1 ) ^{2} ( x ^{2} + 2 x + 2 )}{x + 3}

e x p an d (x - 1) ln (x + 1)

e x p an d e^{3 x - 3} h (x - 1)