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

Lösung

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

- 9 y^{6} sin (3 x)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

- sin (3 x) \frac{\partial}{\partial x} (3 x)

= - sin (3 x) \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (3 x) = 3

= 3 y^{6} (- sin (3 x) \cdot 3)

Vereinfache

= - 9 y^{6} sin (3 x)

\frac{\partial}{\partial x} (2 e^{x y^{2}})

\int \frac{( 3 x - 1 )}{x x ^{2} - 4} d x

x \to 1 lim (7^{x^{4} - x^{2}})

\int_{0}^{1} ln (x + 1) d x

\frac{d}{d x} ((3 + 4 x - x^{2})^{\frac{1}{2}})