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Beliebt Rechnen >

derivative of (2+sin(x)/x)

Lösung

\frac{d}{d x} (\frac{2 + sin ( x )}{x})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{2 + sin ( x )}{x})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

Vereinfache

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

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

Graph

Beliebte Beispiele

tangent f(x)=2x^3-5x,\at x=-1

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

derivative 1/((t^5+4)^4)

d er i v a t i v e \frac{1}{( t ^{5} + 4 ) ^{4}}

derivative of-ln(x-2)

\frac{d}{d x} (- ln (x - 2))

integral of ((x^2-x+8))/(x^3+2x)

\int \frac{( x ^{2} - x + 8 )}{x ^{3} + 2 x} d x

6t((dy)/(dt))+5y=sqrt(t)

6 t (\frac{d y}{d t}) + 5 y = t