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

解

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

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

解答ステップ

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

y

を定数として扱う

積の法則を適用:

(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}

簡素化

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