derivative of x^2sqrt(2x+3)

解

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

\frac{5 x ^{2} + 6 x}{2 x + 3}

解答ステップ

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

積の法則を適用:

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

f = x^{2}, g = 2 x + 3

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

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

\frac{d}{d x} (2 x + 3) = \frac{1}{2 x + 3}

= 2 x 2 x + 3 + \frac{1}{2 x + 3} x^{2}

簡素化

2 x 2 x + 3 + \frac{1}{2 x + 3} x^{2} : \frac{5 x ^{2} + 6 x}{2 x + 3}

= \frac{5 x ^{2} + 6 x}{2 x + 3}