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

Lösung

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

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

Schritte zur Lösung

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

\frac{d}{d x} (y (3 x - 4)) = \frac{d y}{d x} (3 x - 4) + 3 y

= \frac{d}{d x} (\frac{d y}{d x} (3 x - 4) + 3 y)

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

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

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

e x p an d (2 x - y + 3 z = 10) \cdot (- 3)

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

e x p an d \frac{1}{( a - b ) ( a + b )}

e x p an d (y^{4}) x^{3} (3 e^{x} + C)