derivative f(x)=(5sqrt(x)+9)x^2

解

導関数

f (x) = (5 x + 9) x^{2}

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

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

\frac{5}{2 x} x^{2} = \frac{5 x ^{\frac{3}{2}}}{2}

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