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

Lösung

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

cos (y) (cos (x) - x sin (x))

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = cos (x)

= cos (y) (\frac{\partial}{\partial x} (x) cos (x) + \frac{\partial}{\partial x} (cos (x)) x)

\frac{\partial}{\partial x} (x) = 1

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

= cos (y) (1 \cdot cos (x) + (- sin (x)) x)

Vereinfache

= cos (y) (cos (x) - x sin (x))

y^{^{'}} = \frac{sec ( y )}{( x - 4 ) ^{2}}

s l o p e in t erce pt (3, - 4), (5, 6)

\frac{d}{d x} (\frac{3}{x + 1})

\int cot (x) csc (x) d x

\int sin (π) x - 3 sin (3 x) d x