d/(dy)((x)(2y^3+x-pi^7-4x^3+cos(3+2y)-5))

解

\frac{d}{d y} ((x) (2 y^{3} + x - π^{7} - 4 x^{3} + cos (3 + 2 y) - 5))

x (6 y^{2} - 2 sin (2 y + 3))

解答ステップ

\frac{d}{d y} ((x) (2 y^{3} + x - π^{7} - 4 x^{3} + cos (3 + 2 y) - 5))

x

を定数として扱う

定数を除去:

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

= x \frac{d}{d y} (2 y^{3} + x - π^{7} - 4 x^{3} + cos (3 + 2 y) - 5)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= x (\frac{d}{d y} (2 y^{3}) + \frac{d x}{d y} - \frac{d}{d y} (π^{7}) - \frac{d}{d y} (4 x^{3}) + \frac{d}{d y} (cos (3 + 2 y)) - \frac{d}{d y} (5))

\frac{d}{d y} (2 y^{3}) = 6 y^{2}

\frac{d x}{d y} = 0

\frac{d}{d y} (π^{7}) = 0

\frac{d}{d y} (4 x^{3}) = 0

\frac{d}{d y} (cos (3 + 2 y)) = - sin (3 + 2 y) \cdot 2

\frac{d}{d y} (5) = 0

= x (6 y^{2} + 0 - 0 - 0 - sin (3 + 2 y) \cdot 2 - 0)

簡素化

= x (6 y^{2} - 2 sin (2 y + 3))