derivative of 2xcos(y)

Lösung

\frac{d}{d x} (2 x cos (y))

2 (cos (y) - x sin (y) \frac{d y}{d x})

Schritte zur Lösung

\frac{d}{d x} (2 x cos (y))

Entferne die Konstante:

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

= 2 \frac{d}{d x} (x cos (y))

Wende die Produktregel an:

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

f = x, g = cos (y)

= 2 (\frac{d x}{d x} cos (y) + \frac{d}{d x} (cos (y)) x)

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

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

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

Vereinfache

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

d er i v a t i v e \frac{12}{x ^{3}}

\int - 8 d x

l a pl a ce t r an s f or m 15 t^{2}

d er i v a t i v e - 4 csc^{2} (x) + 4 sec^{2} (x)

d er i v a t i v e y = (x^{2} + x + 1)^{100}