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Beliebt Rechnen >

(\partial)/(\partial x)(e^{xy}cos(x^2))

Lösung

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

Lösung

e^{x y} y cos (x^{2}) - 2 e^{x y} x sin (x^{2})

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = e^{x y}, g = cos (x^{2})

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

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

\frac{\partial}{\partial x} (cos (x^{2})) = - sin (x^{2}) \cdot 2 x

= e^{x y} y cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) e^{x y}

Vereinfache

= e^{x y} y cos (x^{2}) - 2 e^{x y} x sin (x^{2})

Beliebte Beispiele

xy^2dy=(y^3-x^3)dx

x y^{2} d y = (y^{3} - x^{3}) d x

d/(dθ)(sqrt(1+sin(2θ)))

\frac{d}{d θ} (1 + sin (2 θ))

limit as x approaches 0 of xln(sin(x))

x \to 0 lim (x ln (sin (x)))

integral of 4e^{3x}cos(5x)

\int 4 e^{3 x} cos (5 x) d x

integral from 1 to 16 of \sqrt[4]{x}

\int_{1}^{16} 4 x d x