(d^2)/(dx^2)({f}(x){g}(x))

Lösung

\frac{d ^{2}}{d x ^{2}} (f (x) g (x))

2 \frac{d}{d x} (g (x)) \frac{d}{d x} (f (x)) + g (x) \frac{d ^{2}}{d x ^{2}} (f (x)) + f (x) \frac{d ^{2}}{d x ^{2}} (g (x))

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} (f (x) g (x))

\frac{d}{d x} (f (x) g (x)) = \frac{d}{d x} (f (x)) g (x) + \frac{d}{d x} (g (x)) f (x)

= \frac{d}{d x} (\frac{d}{d x} (f (x)) g (x) + \frac{d}{d x} (g (x)) f (x))

\frac{d}{d x} (\frac{d}{d x} (f (x)) g (x) + \frac{d}{d x} (g (x)) f (x)) = 2 \frac{d}{d x} (g (x)) \frac{d}{d x} (f (x)) + g (x) \frac{d ^{2}}{d x ^{2}} (f (x)) + f (x) \frac{d ^{2}}{d x ^{2}} (g (x))

= 2 \frac{d}{d x} (g (x)) \frac{d}{d x} (f (x)) + g (x) \frac{d ^{2}}{d x ^{2}} (f (x)) + f (x) \frac{d ^{2}}{d x ^{2}} (g (x))

\int cos (2 x) sin (2 x) d x

\int_{0}^{π} 9 cos^{6} (x) d x

\int sin (x^{2} - 1) d x

\frac{d}{d x} (\frac{e ^{x}}{1 - e ^{x}})

\int \frac{5 x ^{2} - x + 17}{( x + 2 ) ( x ^{2} + 9 )} d x