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Beliebt Rechnen >

(\partial)/(\partial x)(2xe^{3xy})

Lösung

\frac{\partial}{\partial x} (2 x e^{3 x y})

Lösung

2 (e^{3 x y} + 3 e^{3 x y} x y)

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x e^{3 x y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 2 \frac{\partial}{\partial x} (x e^{3 x y})

Wende die Produktregel an:

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

f = x, g = e^{3 x y}

= 2 (\frac{\partial}{\partial x} (x) e^{3 x y} + \frac{\partial}{\partial x} (e^{3 x y}) x)

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

\frac{\partial}{\partial x} (e^{3 x y}) = e^{3 x y} \cdot 3 y

= 2 (1 \cdot e^{3 x y} + e^{3 x y} \cdot 3 y x)

Vereinfache

= 2 (e^{3 x y} + 3 e^{3 x y} x y)

Beliebte Beispiele

(sin(x)cos(y))dx+(cos(x)sin(y))dy=0

(sin (x) cos (y)) d x + (cos (x) sin (y)) d y = 0

derivative-x^4-6x^3+8x-6

d er i v a t i v e - x^{4} - 6 x^{3} + 8 x - 6

derivative of x^2arctan(x^3)

\frac{d}{d x} (x^{2} arctan (x^{3}))

tangent x^3+4x^2+7x+1

t an g e n t x^{3} + 4 x^{2} + 7 x + 1

sum from n=2 to infinity of 6/(7^n)

n = 2 \sum \infty \frac{6}{7 ^{n}}