derivative of (-cos(x-1)/(x^3+x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

t an g e n t y = 1 + 4 x^{2} - 2 x^{3}

\frac{\partial}{\partial y} (x^{3} - x y^{2} + 3 y^{2})

t an g e n t y = 4 x^{3} - 2 x, (1, 2)

t an g e n t f (x) = x^{2} + 1, (- 4, 17)

2 x y + x^{2} \frac{d y}{d x} = y^{2}