derivative of (x^2+xcos(5x))

Lösung

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

cos (5 x) (2 x + 1) - 5 sin (5 x) (x^{2} + x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (x^{2} + x) = 2 x + 1

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= (2 x + 1) cos (5 x) + (- sin (5 x) \cdot 5) (x^{2} + x)

Vereinfache

= cos (5 x) (2 x + 1) - 5 sin (5 x) (x^{2} + x)

\int \frac{\frac{1}{x} + 1}{x ^{2}} d x

t an g e n t f (x) = 4 3 x, at x = 1

\int_{3}^{3} (x + 1) d x

d er i v a t i v e \frac{7}{5 x}

\frac{d}{d x} (x^{2} - 5 x + \frac{1}{x ^{\frac{3}{2}}})