derivative f(x)=sin(x)-1/3 sin(3x)+1/5 sin(5x)

Lösung

ableitung von

f (x) = sin (x) - \frac{1}{3} sin (3 x) + \frac{1}{5} sin (5 x)

cos (x) - cos (3 x) + cos (5 x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sin (x)) - \frac{d}{d x} (\frac{1}{3} sin (3 x)) + \frac{d}{d x} (\frac{1}{5} sin (5 x))

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

\frac{d}{d x} (\frac{1}{3} sin (3 x)) = cos (3 x)

\frac{d}{d x} (\frac{1}{5} sin (5 x)) = cos (5 x)

= cos (x) - cos (3 x) + cos (5 x)

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

l a pl a ce t r an s f or m sin (y)

\int \frac{1}{x ( x + 4 )} d x

\int x \cdot 9^{2 x^{2} - 8} d x

\int x 3 4 + x^{2} d x