derivative of axsin(x)

Lösung

\frac{d}{d x} (a x sin (x))

a (sin (x) + x cos (x))

Schritte zur Lösung

\frac{d}{d x} (a x sin (x))

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = sin (x)

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

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

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

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

Vereinfache

= a (sin (x) + x cos (x))

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

(\frac{d y}{d t}) - (\frac{3}{t}) \cdot y = 2 t^{3} e^{2 t}, y (1) = 0

d er i v a t i v e f (x) = 7 x^{2} + 6 x

t an g e n t - 2 x^{2}, at x = - 2

in v erse l a pl a ce \frac{12}{s ^{2} - 5}