(\partial)/(\partial x)(4xcos(xy))

Lösung

\frac{\partial}{\partial x} (4 x cos (x y))

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

Schritte zur Lösung

\frac{\partial}{\partial x} (4 x cos (x y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 4 \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)

= 4 (\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

= 4 (1 \cdot cos (x y) + (- sin (x y) y) x)

Vereinfache

= 4 (cos (x y) - x y sin (x y))

\int \frac{4 + 7 x}{1 + x ^{2}} d x

\int_{0}^{1} \frac{1}{16 - x ^{2}} d x

y d x + x^{2} + 1 d y = 0

\frac{d}{d x} ((5 - 3 x)^{2})

\int \frac{1}{( 1 + x ) ^{\frac{3}{4}}} d x