derivative f(x)=x^4sin(4x)

Lösung

ableitung von

f (x) = x^{4} sin (4 x)

4 x^{3} sin (4 x) + cos (4 x) \cdot 4 x^{4}

Schritte zur Lösung

\frac{d}{d x} (x^{4} sin (4 x))

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (sin (4 x)) = cos (4 x) \cdot 4

= 4 x^{3} sin (4 x) + cos (4 x) \cdot 4 x^{4}

\int_{1}^{2} 1

n = 0 \sum \infty \frac{π ^{n}}{e ^{n}}

t \to 1 lim (7 e^{t} - 3)

a re a y = \frac{x ^{2} + 4}{3 x - x ^{2}}, (1, 2)

d er i v a t i v e (arccot (x))^{5}