(\partial)/(\partial x)((1+x^2)^{zsin(y)})

Lösung

\frac{\partial}{\partial x} ((1 + x^{2})^{z s i n (y)})

z sin (y) (1 + x^{2})^{z s i n (y) - 1} \cdot 2 x

Schritte zur Lösung

\frac{\partial}{\partial x} ((1 + x^{2})^{z s i n (y)})

Behandle

z, y

als Konstanten

Wende die Kettenregel an:

z sin (y) (1 + x^{2})^{z s i n (y) - 1} \frac{\partial}{\partial x} (1 + x^{2})

= z sin (y) (1 + x^{2})^{z s i n (y) - 1} \frac{\partial}{\partial x} (1 + x^{2})

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

= z sin (y) (1 + x^{2})^{z s i n (y) - 1} \cdot 2 x

t an g e n t f (x) = \frac{( x + 1 )}{( x - 1 )}

\int_{1}^{x} \frac{2}{x ^{3}} d x

t an g e n t y = \frac{x - 1}{x + 1}

\frac{d}{d x} (7 x^{- 6} - 5 x^{- 3})

d er i v a t i v e y = - 10