d/(dp)(e^p(p+psqrt(p)))

解

\frac{d}{d p} (e^{p} (p + p p))

e^{p} (p + p^{\frac{3}{2}}) + (1 + \frac{3 p}{2}) e^{p}

解答ステップ

\frac{d}{d p} (e^{p} (p + p p))

簡素化

e^{p} (p + p p) : e^{p} (p + p^{\frac{3}{2}})

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

積の法則を適用:

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

f = e^{p}, g = p + p^{\frac{3}{2}}

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

\frac{d}{d p} (e^{p}) = e^{p}

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

= e^{p} (p + p^{\frac{3}{2}}) + (1 + \frac{3 p}{2}) e^{p}