(\partial)/(\partial x)(cos^9(x^4y^8))

Lösung

\frac{\partial}{\partial x} (cos^{9} (x^{4} y^{8}))

- 36 x^{3} y^{8} cos^{8} (x^{4} y^{8}) sin (x^{4} y^{8})

Schritte zur Lösung

\frac{\partial}{\partial x} (cos^{9} (x^{4} y^{8}))

Behandle

y

als Konstante

Wende die Kettenregel an:

9 (cos (x^{4} y^{8}))^{8} \frac{\partial}{\partial x} (cos (x^{4} y^{8}))

= 9 (cos (x^{4} y^{8}))^{8} \frac{\partial}{\partial x} (cos (x^{4} y^{8}))

\frac{\partial}{\partial x} (cos (x^{4} y^{8})) = - sin (x^{4} y^{8}) \cdot 4 y^{8} x^{3}

= 9 (cos (x^{4} y^{8}))^{8} (- sin (x^{4} y^{8}) \cdot 4 y^{8} x^{3})

Vereinfache

= - 36 x^{3} y^{8} cos^{8} (x^{4} y^{8}) sin (x^{4} y^{8})

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

\frac{d}{d t} (\frac{t ^{2}}{2})

\frac{d}{d x} (e^{(x^{2} - x)})

\int_{0}^{3} x - (x^{2} - 2 x) d x

\int 7 + 6 x - x^{2} d x