(\partial)/(\partial x)(cos^6(x^7y^8))

Lösung

\frac{\partial}{\partial x} (cos^{6} (x^{7} y^{8}))

- 42 x^{6} y^{8} cos^{5} (x^{7} y^{8}) sin (x^{7} y^{8})

Schritte zur Lösung

\frac{\partial}{\partial x} (cos^{6} (x^{7} y^{8}))

Behandle

y

als Konstante

Wende die Kettenregel an:

6 (cos (x^{7} y^{8}))^{5} \frac{\partial}{\partial x} (cos (x^{7} y^{8}))

= 6 (cos (x^{7} y^{8}))^{5} \frac{\partial}{\partial x} (cos (x^{7} y^{8}))

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

= 6 (cos (x^{7} y^{8}))^{5} (- sin (x^{7} y^{8}) \cdot 7 y^{8} x^{6})

Vereinfache

= - 42 x^{6} y^{8} cos^{5} (x^{7} y^{8}) sin (x^{7} y^{8})