(\partial)/(\partial x)(cos^9(x^8y^6))

Lösung

\frac{\partial}{\partial x} (cos^{9} (x^{8} y^{6}))

- 72 x^{7} y^{6} cos^{8} (x^{8} y^{6}) sin (x^{8} y^{6})

Schritte zur Lösung

\frac{\partial}{\partial x} (cos^{9} (x^{8} y^{6}))

Behandle

y

als Konstante

Wende die Kettenregel an:

9 (cos (x^{8} y^{6}))^{8} \frac{\partial}{\partial x} (cos (x^{8} y^{6}))

= 9 (cos (x^{8} y^{6}))^{8} \frac{\partial}{\partial x} (cos (x^{8} y^{6}))

\frac{\partial}{\partial x} (cos (x^{8} y^{6})) = - sin (x^{8} y^{6}) \cdot 8 y^{6} x^{7}

= 9 (cos (x^{8} y^{6}))^{8} (- sin (x^{8} y^{6}) \cdot 8 y^{6} x^{7})

Vereinfache

= - 72 x^{7} y^{6} cos^{8} (x^{8} y^{6}) sin (x^{8} y^{6})

d er i v a t i v e 4^{\frac{c}{x}}

\int_{0}^{\infty} x e^{- \frac{x}{9}} d x

x \to \infty lim (- 3)

\frac{\partial}{\partial x} (\frac{3 x + 2 x y}{7 x + 6 y})

\int 6 tan^{3} (x) d x