(\partial)/(\partial x)(cos(x^2+y^2)*2x)

解

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

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

解答ステップ

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

y

を定数として扱う

定数を除去:

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

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

積の法則を適用:

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

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

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

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

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

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

簡素化

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

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