derivative (5x^2+3)^{1/4}

解

導関数

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

\frac{5 x}{2 ( 5 x ^{2} + 3 ) ^{\frac{3}{4}}}

解答ステップ

\frac{d}{d x} ((5 x^{2} + 3)^{\frac{1}{4}})

連鎖法則を適用:

\frac{1}{4 ( 5 x ^{2} + 3 ) ^{\frac{3}{4}}} \frac{d}{d x} (5 x^{2} + 3)

= \frac{1}{4 ( 5 x ^{2} + 3 ) ^{\frac{3}{4}}} \frac{d}{d x} (5 x^{2} + 3)

\frac{d}{d x} (5 x^{2} + 3) = 10 x

= \frac{1}{4 ( 5 x ^{2} + 3 ) ^{\frac{3}{4}}} \cdot 10 x

簡素化

\frac{1}{4 ( 5 x ^{2} + 3 ) ^{\frac{3}{4}}} \cdot 10 x : \frac{5 x}{2 ( 5 x ^{2} + 3 ) ^{\frac{3}{4}}}

= \frac{5 x}{2 ( 5 x ^{2} + 3 ) ^{\frac{3}{4}}}