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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (tan (x) + x) = sec^{2} (x) + 1

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

Graph

Beliebte Beispiele

derivative 1/((3x+7))

d er i v a t i v e \frac{1}{( 3 x + 7 )}

tangent 1/(4+3x)

t an g e n t \frac{1}{4 + 3 x}

derivative of ln(x+a)

\frac{d}{d x} (ln (x + a))

integral of ((2x+1))/(sqrt(x+4))

\int \frac{( 2 x + 1 )}{x + 4} d x

derivative of sqrt(e^{x^3)}

\frac{d}{d x} (e^{x^{3}})