derivative of (9sqrt(x)+5x^2)

解

\frac{d}{d x} ((9 x + 5) x^{2})

\frac{9 x ^{\frac{3}{2}}}{2} + 2 x (9 x + 5)

解答ステップ

\frac{d}{d x} ((9 x + 5) x^{2})

積の法則を適用:

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

f = 9 x + 5, g = x^{2}

= \frac{d}{d x} (9 x + 5) x^{2} + \frac{d}{d x} (x^{2}) (9 x + 5)

\frac{d}{d x} (9 x + 5) = \frac{9}{2 x}

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

= \frac{9}{2 x} x^{2} + 2 x (9 x + 5)

\frac{9}{2 x} x^{2} = \frac{9 x ^{\frac{3}{2}}}{2}

= \frac{9 x ^{\frac{3}{2}}}{2} + 2 x (9 x + 5)