derivative of x,x^2-y,x+y^2

解

\frac{d}{d x} (x, x^{2} - y, x + y^{2})

(, (1 \cdot x^{2} + 2 xx)) - (, (\frac{d y}{d x} x + 1 \cdot y)) + 2 y \frac{d y}{d x}

解答ステップ

\frac{d}{d x} (x, x^{2} - y, x + y^{2})

和/差の法則を適用:

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

= \frac{d}{d x} (x, x^{2}) - \frac{d}{d x} (y, x) + \frac{d}{d x} (y^{2})

\frac{d}{d x} (x, x^{2}) = (, (1 \cdot x^{2} + 2 xx))

\frac{d}{d x} (y, x) = (, (\frac{d y}{d x} x + 1 \cdot y))

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

= (, (1 \cdot x^{2} + 2 xx)) - (, (\frac{d y}{d x} x + 1 \cdot y)) + 2 y \frac{d y}{d x}