(\partial)/(\partial x)(cos^6(x^9y^3))

Lösung

\frac{\partial}{\partial x} (cos^{6} (x^{9} y^{3}))

- 54 x^{8} y^{3} cos^{5} (x^{9} y^{3}) sin (x^{9} y^{3})

Schritte zur Lösung

\frac{\partial}{\partial x} (cos^{6} (x^{9} y^{3}))

Behandle

y

als Konstante

Wende die Kettenregel an:

6 (cos (x^{9} y^{3}))^{5} \frac{\partial}{\partial x} (cos (x^{9} y^{3}))

= 6 (cos (x^{9} y^{3}))^{5} \frac{\partial}{\partial x} (cos (x^{9} y^{3}))

\frac{\partial}{\partial x} (cos (x^{9} y^{3})) = - sin (x^{9} y^{3}) \cdot 9 y^{3} x^{8}

= 6 (cos (x^{9} y^{3}))^{5} (- sin (x^{9} y^{3}) \cdot 9 y^{3} x^{8})

Vereinfache

= - 54 x^{8} y^{3} cos^{5} (x^{9} y^{3}) sin (x^{9} y^{3})

\int 9 + 16 x^{2} d x

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\frac{d}{d x} (34 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x))

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