derivative of-(x+1sin((x^2)/2))

Lösung

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

- sin (\frac{x ^{2}}{2}) - x^{2} cos (\frac{x ^{2}}{2}) - x cos (\frac{x ^{2}}{2})

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} ((x + 1) sin (\frac{x ^{2}}{2}))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + 1, g = sin (\frac{x ^{2}}{2})

= - (\frac{d}{d x} (x + 1) sin (\frac{x ^{2}}{2}) + \frac{d}{d x} (sin (\frac{x ^{2}}{2})) (x + 1))

\frac{d}{d x} (x + 1) = 1

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

= - (1 \cdot sin (\frac{x ^{2}}{2}) + cos (\frac{x ^{2}}{2}) x (x + 1))

Vereinfache

- (1 \cdot sin (\frac{x ^{2}}{2}) + cos (\frac{x ^{2}}{2}) x (x + 1)) : - sin (\frac{x ^{2}}{2}) - x^{2} cos (\frac{x ^{2}}{2}) - x cos (\frac{x ^{2}}{2})

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

s l o p e y = 6 sin (π x - y), (1, 0)

\int 2 cos (2 x) - 1 d x

l a pl a ce t r an s f or m cos^{2} (2 t)

\int 2 x (x^{2} + 3)^{7} d x

ma c l a u r in x - e^{3 x}