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

Lösung

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

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

Schritte zur Lösung

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

\frac{d}{d x} (y (cos (x) + 2)) = \frac{d y}{d x} (cos (x) + 2) - sin (x) y

= \frac{d ^{3}}{d x ^{3}} (\frac{d y}{d x} (cos (x) + 2) - sin (x) y)

\frac{d}{d x} (\frac{d y}{d x} (cos (x) + 2) - sin (x) y) = cos (x) \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d ^{2} y}{d x ^{2}} - 2 sin (x) \frac{d y}{d x} - cos (x) y

= \frac{d ^{2}}{d x ^{2}} (cos (x) \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d ^{2} y}{d x ^{2}} - 2 sin (x) \frac{d y}{d x} - cos (x) y)

\frac{d}{d x} (cos (x) \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d ^{2} y}{d x ^{2}} - 2 sin (x) \frac{d y}{d x} - cos (x) y) = - 3 sin (x) \frac{d ^{2} y}{d x ^{2}} + cos (x) \frac{d ^{3} y}{d x ^{3}} + 2 \frac{d ^{3} y}{d x ^{3}} - 3 cos (x) \frac{d y}{d x} + sin (x) y

= \frac{d}{d x} (- 3 sin (x) \frac{d ^{2} y}{d x ^{2}} + cos (x) \frac{d ^{3} y}{d x ^{3}} + 2 \frac{d ^{3} y}{d x ^{3}} - 3 cos (x) \frac{d y}{d x} + sin (x) y)

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

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

e x p an d \frac{s ^{2} - 4}{( s ^{2} - 4 s + 5 ) ^{2}}

e x p an d (- (\frac{3 x}{4} + 3) cos (\frac{3 x}{4} + 3)) + sin (\frac{3 x}{4} + 3)

e x p an d 2.5 x^{2.5 x - 0.5} (0.5 ln (x) + 1)

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

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