(d^3)/(dx^3)((y)(4x^2-6x+2))

Lösung

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

4 x^{2} \frac{d ^{3} y}{d x ^{3}} - 6 x \frac{d ^{3} y}{d x ^{3}} + 24 x \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d ^{3} y}{d x ^{3}} - 18 \frac{d ^{2} y}{d x ^{2}} + 24 \frac{d y}{d x}

Schritte zur Lösung

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

\frac{d}{d x} (y (4 x^{2} - 6 x + 2)) = \frac{d y}{d x} (4 x^{2} - 6 x + 2) + (8 x - 6) y

= \frac{d ^{2}}{d x ^{2}} (\frac{d y}{d x} (4 x^{2} - 6 x + 2) + (8 x - 6) y)

\frac{d}{d x} (\frac{d y}{d x} (4 x^{2} - 6 x + 2) + (8 x - 6) y) = \frac{d ^{2} y}{d x ^{2}} (4 x^{2} - 6 x + 2) + 2 \frac{d y}{d x} (8 x - 6) + 8 y

= \frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}} (4 x^{2} - 6 x + 2) + 2 \frac{d y}{d x} (8 x - 6) + 8 y)

\frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}} (4 x^{2} - 6 x + 2) + 2 \frac{d y}{d x} (8 x - 6) + 8 y) = 4 x^{2} \frac{d ^{3} y}{d x ^{3}} - 6 x \frac{d ^{3} y}{d x ^{3}} + 24 x \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d ^{3} y}{d x ^{3}} - 18 \frac{d ^{2} y}{d x ^{2}} + 24 \frac{d y}{d x}

= 4 x^{2} \frac{d ^{3} y}{d x ^{3}} - 6 x \frac{d ^{3} y}{d x ^{3}} + 24 x \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d ^{3} y}{d x ^{3}} - 18 \frac{d ^{2} y}{d x ^{2}} + 24 \frac{d y}{d x}

e x p an d sin (x) (1 + cot (x) = sin (x) + cos (x))

e x p an d \frac{8}{x ( x ^{2} + 4 )}

e x p an d \frac{10}{s ( s + 1 ) ( s + 10 )}

e x p an d (t + e^{3 t})^{2}

s im pl i f y 3 (2 + 5)