(\partial)/(\partial x)(400sin(x)cos(x))

Lösung

\frac{\partial}{\partial x} (400 \cdot sin (x) \cdot cos (x))

400 cos (2 x)

Schritte zur Lösung

\frac{\partial}{\partial x} (400 sin (x) cos (x))

Entferne die Konstante:

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

= 400 \frac{\partial}{\partial x} (sin (x) cos (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x), g = cos (x)

= 400 (\frac{\partial}{\partial x} (sin (x)) cos (x) + \frac{\partial}{\partial x} (cos (x)) sin (x))

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

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

= 400 (cos (x) cos (x) + (- sin (x)) sin (x))

Vereinfache

400 (cos (x) cos (x) + (- sin (x)) sin (x)) : 400 cos (2 x)

= 400 cos (2 x)

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

y^{^{'}} = x^{2} e^{2 y}, y (- 1) = - 1

\frac{d}{d t} (3 cos (t) - 2 e^{2 t})

s l o p e in t erce pt (- 1, 0), (0, - 2)

(x^{2} + 3 x y + y^{2}) d x - x^{2} d y = 0