derivative of 4x^2cos(2x)

Lösung

\frac{d}{d x} (4 x^{2} cos (2 x))

4 (2 x cos (2 x) - 2 x^{2} sin (2 x))

Schritte zur Lösung

\frac{d}{d x} (4 x^{2} cos (2 x))

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x^{2} cos (2 x))

Wende die Produktregel an:

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

f = x^{2}, g = cos (2 x)

= 4 (\frac{d}{d x} (x^{2}) cos (2 x) + \frac{d}{d x} (cos (2 x)) x^{2})

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

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

= 4 (2 x cos (2 x) + (- sin (2 x) \cdot 2) x^{2})

Vereinfache

= 4 (2 x cos (2 x) - 2 x^{2} sin (2 x))

\frac{d y}{d x} = x + y - 1

in v erse l a pl a ce \frac{1}{s ^{3} ( s + 4 )}

\frac{d}{d x} (10 x^{10} e^{x})

\int \frac{1}{- t ^{2} + 8 t - 15} d t

d er i v a t i v e x + e^{x} - \frac{1}{x}