d/(d{x)}({x}^3+2{x}{y}+{y}^2+{z}^2-5{x}-4{z})

解

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

3 x^{2} + 2 y - 5

解答ステップ

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

和/差の法則を適用:

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

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (2 x y) = 2 y

\frac{d}{d x} (y^{2}) = 0

\frac{d}{d x} (z^{2}) = 0

\frac{d}{d x} (5 x) = 5

\frac{d}{d x} (4 z) = 0

= 3 x^{2} + 2 y + 0 + 0 - 5 - 0

簡素化

= 3 x^{2} + 2 y - 5