(\partial)/(\partial x)(x*sin(x^2-y^2))

解

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

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

解答ステップ

\frac{\partial}{\partial x} (x sin (x^{2} - y^{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 = x, g = sin (x^{2} - y^{2})

= \frac{\partial}{\partial x} (x) sin (x^{2} - y^{2}) + \frac{\partial}{\partial x} (sin (x^{2} - y^{2})) x

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

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

= 1 \cdot sin (x^{2} - y^{2}) + cos (x^{2} - y^{2}) \cdot 2 xx

簡素化

1 \cdot sin (x^{2} - y^{2}) + cos (x^{2} - y^{2}) \cdot 2 xx : sin (x^{2} - y^{2}) + 2 x^{2} cos (x^{2} - y^{2})

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