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Beliebt Rechnen >

derivative 1/x sin(x)

Lösung

ableitung von

\frac{1}{x} sin (x)

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x} sin (x))

Wende die Produktregel an:

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

f = \frac{1}{x}, g = sin (x)

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of (sin(12x)/(e^{7x)})

\frac{d}{d x} (\frac{sin ( 12 x )}{e ^{7 x}})

integral of 16tan^4(x)sec^6(x)

\int 16 tan^{4} (x) sec^{6} (x) d x

tangent f(x)=38-x^2,(-6,2)

t an g e n t f (x) = 38 - x^{2}, (- 6, 2)

tangent y=3-x^3(0.3)

t an g e n t y = 3 - x^{3} (0.3)

integral of x^2(x^3-1)^2

\int x^{2} (x^{3} - 1)^{2} d x