derivative f(x)=x^{3/2}+sqrt(x+4)

解

導関数

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

\frac{3 x ^{\frac{1}{2}}}{2} + \frac{1}{2 ( x + 4 ) ^{\frac{1}{2}}}

解答ステップ

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

和/差の法則を適用:

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

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

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

\frac{d}{d x} (x + 4) = \frac{1}{2 ( x + 4 ) ^{\frac{1}{2}}}

= \frac{3 x ^{\frac{1}{2}}}{2} + \frac{1}{2 ( x + 4 ) ^{\frac{1}{2}}}