derivative of 5x^2cos(7x)

Lösung

\frac{d}{d x} (5 x^{2} cos (7 x))

5 (2 x cos (7 x) - 7 x^{2} sin (7 x))

Schritte zur Lösung

\frac{d}{d x} (5 x^{2} cos (7 x))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x^{2} cos (7 x))

Wende die Produktregel an:

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

f = x^{2}, g = cos (7 x)

= 5 (\frac{d}{d x} (x^{2}) cos (7 x) + \frac{d}{d x} (cos (7 x)) x^{2})

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

\frac{d}{d x} (cos (7 x)) = - sin (7 x) \cdot 7

= 5 (2 x cos (7 x) + (- sin (7 x) \cdot 7) x^{2})

Vereinfache

= 5 (2 x cos (7 x) - 7 x^{2} sin (7 x))

f^{^{''}} (x) = x^{3} - 4 x + 1, f^{^{'}} (0) = 2, f (1) = - 2

x \to 2 lim (x^{2} - 5 x + 6 x^{2} - 4)

x \to 7 lim (\frac{x + 7}{x - 7})

\int cos (8 x) cos (3 x) d x

\int \frac{3}{t} d t