derivative of 9x^5cos(x)

Lösung

\frac{d}{d x} (9 x^{5} cos (x))

9 (5 x^{4} cos (x) - x^{5} sin (x))

Schritte zur Lösung

\frac{d}{d x} (9 x^{5} cos (x))

Entferne die Konstante:

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

= 9 \frac{d}{d x} (x^{5} cos (x))

Wende die Produktregel an:

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

f = x^{5}, g = cos (x)

= 9 (\frac{d}{d x} (x^{5}) cos (x) + \frac{d}{d x} (cos (x)) x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 9 (5 x^{4} cos (x) + (- sin (x)) x^{5})

Vereinfache

= 9 (5 x^{4} cos (x) - x^{5} sin (x))

\frac{d}{d x} (x + x^{5})

ma c l a u r in \frac{1}{1 + x ^{4}}

a re a y = e^{x}, y = x, x = 0, x = 1

\int \frac{e ^{2 x}}{1 - e ^{4 x}} d x

x \to 2 lim (\frac{x + 1}{x ^{2} - 4})