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

Lösung

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

\frac{3 sin ( 2 x )}{( cos ^{2} ( x ) + 1 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{sin ( 2 x ) ( cos ^{2} ( x ) + 1 ) - ( - sin ( 2 x ) ) ( sin ^{2} ( x ) + 1 )}{( cos ^{2} ( x ) + 1 ) ^{2}} : \frac{3 sin ( 2 x )}{( cos ^{2} ( x ) + 1 ) ^{2}}

= \frac{3 sin ( 2 x )}{( cos ^{2} ( x ) + 1 ) ^{2}}

d er i v a t i v e \frac{x}{8}

in v erse l a pl a ce {\frac{( s - 1 )}{s + 1}}

\frac{\partial}{\partial y} (e^{x y} + x^{2} z)

d er i v a t i v e \frac{x ^{4}}{1 - x ^{3}}

a re a x^{2}, (- 2, 1)