derivative of (5x^4+2(3sin(x)))

Lösung

\frac{d}{d x} ((5 x^{4} + 2) (3 sin (x)))

3 (20 x^{3} sin (x) + cos (x) (5 x^{4} + 2))

Schritte zur Lösung

\frac{d}{d x} ((5 x^{4} + 2) (3 sin (x)))

Entferne die Konstante:

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

= 3 \frac{d}{d x} ((5 x^{4} + 2) sin (x))

Wende die Produktregel an:

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

f = 5 x^{4} + 2, g = sin (x)

= 3 (\frac{d}{d x} (5 x^{4} + 2) sin (x) + \frac{d}{d x} (sin (x)) (5 x^{4} + 2))

\frac{d}{d x} (5 x^{4} + 2) = 20 x^{3}

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

= 3 (20 x^{3} sin (x) + cos (x) (5 x^{4} + 2))

d er i v a t i v e \frac{8}{x ^{4}}

\frac{d}{d x} (e^{- 8 x} sin (8 x))

\int 3 e^{t} d t

x \to - 2 - lim (\frac{3}{x + 2})

\frac{d}{d x} (\frac{1 - x}{e ^{2 x}})