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Beliebt Rechnen >

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

Lösung

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

Lösung

4 (sin (x y) + x y cos (x y))

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = sin (x y)

= 4 (\frac{\partial}{\partial x} (x) sin (x y) + \frac{\partial}{\partial x} (sin (x y)) x)

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

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

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

Vereinfache

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

Beliebte Beispiele

(\partial)/(\partial x)(3x^2+xy+y^2-8)

\frac{\partial}{\partial x} (3 x^{2} + x y + y^{2} - 8)

derivative of log_{e}(3x)

\frac{d}{d x} (lo g_{e} (3 x))

(\partial)/(\partial y)(xe^{2xy})

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

y^'+8y=1,y(0)=1

y^{^{'}} + 8 y = 1, y (0) = 1

derivative of (x-5/(4x^2e^x))

\frac{d}{d x} (\frac{x - 5}{4 x ^{2} e ^{x}})