(\partial)/(\partial x)(x^3+4x^2+x^4+3x^5)

解

\frac{\partial}{\partial x} (x^{3} + 4 x^{2} + x^{4} + 3 x^{5})

3 x^{2} + 8 x + 4 x^{3} + 15 x^{4}

解答ステップ

\frac{\partial}{\partial x} (x^{3} + 4 x^{2} + x^{4} + 3 x^{5})

和/差の法則を適用:

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

= \frac{\partial}{\partial x} (x^{3}) + \frac{\partial}{\partial x} (4 x^{2}) + \frac{\partial}{\partial x} (x^{4}) + \frac{\partial}{\partial x} (3 x^{5})

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

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

\frac{\partial}{\partial x} (3 x^{5}) = 15 x^{4}

= 3 x^{2} + 8 x + 4 x^{3} + 15 x^{4}