derivative f(x)=x^2-2/x+3*sin(2x)

Lösung

ableitung von

f (x) = x^{2} - \frac{2}{x} + 3 \cdot sin (2 x)

2 x + \frac{2}{x ^{2}} + 6 cos (2 x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{2}) - \frac{d}{d x} (\frac{2}{x}) + \frac{d}{d x} (3 sin (2 x))

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

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

\frac{d}{d x} (3 sin (2 x)) = 6 cos (2 x)

= 2 x - (- \frac{2}{x ^{2}}) + 6 cos (2 x)

Vereinfache

= 2 x + \frac{2}{x ^{2}} + 6 cos (2 x)

s im pl i f y (0) (2.6)

d er i v a t i v e f (x) = \frac{3}{x ^{4}}

d er i v a t i v e y = x^{(\frac{7}{3})}

t an g e n t x^{2} + 3 x - 5, at x = 1

s l o p e y = 7 x