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Beliebt Rechnen >

(\partial)/(\partial x)(y^6cos(4x)*4)

Lösung

\frac{\partial}{\partial x} (y^{6} cos (4 x) \cdot 4)

Lösung

- 16 y^{6} sin (4 x)

Schritte zur Lösung

\frac{\partial}{\partial x} (y^{6} cos (4 x) \cdot 4)

Behandle

y

als Konstante

Entferne die Konstante:

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

= y^{6} \cdot 4 \frac{\partial}{\partial x} (cos (4 x))

Wende die Kettenregel an:

- sin (4 x) \frac{\partial}{\partial x} (4 x)

= - sin (4 x) \frac{\partial}{\partial x} (4 x)

\frac{\partial}{\partial x} (4 x) = 4

= y^{6} \cdot 4 (- sin (4 x) \cdot 4)

Vereinfache

= - 16 y^{6} sin (4 x)

Beliebte Beispiele

sum from n=1 to infinity of 9/(100^n)

n = 1 \sum \infty \frac{9}{10 0 ^{n}}

limit as x approaches 0 of g(x)

x \to 0 lim (g (x))

(\partial)/(\partial x)(2xy)

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

integral of e^{7x}sin(7x)

\int e^{7 x} sin (7 x) d x

(dy)/(dx)=x^6(y-2),y(0)=6

\frac{d y}{d x} = x^{6} (y - 2), y (0) = 6