(\partial)/(\partial x)(cos^2(x)y)

Lösung

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

- y sin (2 x)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

= y \frac{\partial}{\partial x} (cos^{2} (x))

Wende die Kettenregel an:

2 cos (x) \frac{\partial}{\partial x} (cos (x))

= 2 cos (x) \frac{\partial}{\partial x} (cos (x))

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

= y \cdot 2 cos (x) (- sin (x))

Vereinfache

y \cdot 2 cos (x) (- sin (x)) : - y sin (2 x)

= - y sin (2 x)

\frac{d}{d a} (sec (a) \cdot tan (a) \cdot cos (a) \cdot csc (a))

\int \frac{e ^{9 x}}{e ^{9 x} + 1} d x

f (x) = sin (x + 1)

\int 3 y^{2} \frac{1}{2 y} tan (2 y x) d x

\int 6 x^{- 1} d x