derivative of (x-1sin(x))

Lösung

\frac{d}{d x} ((x - 1) sin (x))

sin (x) + cos (x) (x - 1)

Schritte zur Lösung

\frac{d}{d x} ((x - 1) sin (x))

Wende die Produktregel an:

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

f = x - 1, g = sin (x)

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

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

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

= 1 \cdot sin (x) + cos (x) (x - 1)

Vereinfache

= sin (x) + cos (x) (x - 1)

\frac{\partial}{\partial x} (ln (e^{x} + e^{y}))

\frac{d}{d y} (1 + y e^{x y})

\int x tan (π x) d x

\frac{\partial}{\partial x} (sin (4 x - 2 y))

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