derivative of cos(x+sin(x)+1/2 x^2+1/x)

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

cos (x) + sin (x) + \frac{1}{2} x^{2} + \frac{1}{x} : cos (x) + sin (x) + \frac{x ^{2}}{2} + \frac{1}{x}

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

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

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

\int_{2}^{5} \frac{1}{x - 1} d x

\int \frac{x}{k} d x

d er i v a t i v e (4 t^{2} - t) (t^{3} - 8 t^{2} + 12)

x \to π - lim (\frac{x}{cos ( x ) + 1})