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Beliebt Rechnen >

(\partial)/(\partial x)(7xcos(xy))

Lösung

\frac{\partial}{\partial x} (7 x cos (x y))

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} (7 x cos (x y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 7 \frac{\partial}{\partial x} (x cos (x y))

Wende die Produktregel an:

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

f = x, g = cos (x y)

= 7 (\frac{\partial}{\partial x} (x) cos (x y) + \frac{\partial}{\partial x} (cos (x y)) x)

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

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

= 7 (1 \cdot cos (x y) + (- sin (x y) y) x)

Vereinfache

= 7 (cos (x y) - x y sin (x y))

Beliebte Beispiele

7 y^{^{''}} + y = 0

integral of e^{4x} 1/5

\int e^{4 x} \frac{1}{5} d x

(dy)/(dt)=(5+sin(t))*(y/5)

\frac{d y}{d t} = (5 + sin (t)) \cdot (\frac{y}{5})

integral of (x+11)/((x-4)(x+1))

\int \frac{x + 11}{( x - 4 ) ( x + 1 )} d x

derivative y=sqrt(ax+b)

d er i v a t i v e y = a x + b