derivative of xsin(x+y)

Lösung

\frac{d}{d x} (x sin (x + y))

sin (x + y) + x cos (x + y) (1 + \frac{d y}{d x})

Schritte zur Lösung

\frac{d}{d x} (x sin (x + y))

Wende die Produktregel an:

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

f = x, g = sin (x + y)

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

\frac{d x}{d x} = 1

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

= 1 \cdot sin (x + y) + cos (x + y) (1 + \frac{d y}{d x}) x

Vereinfache

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

\int \frac{x}{x ^{2} + 2 x + 25} d x

\int \frac{5 x + 7}{4 x ^{2} + 12 x + 10} d x

d er i v a t i v e f (t) = \frac{( e ^{x} + 5 x )}{5 x}

a re a x^{2} + 2, 2 x + 6

\int 10 tan^{2} (x) d x