derivative \sqrt[4]{2x^{12}+sin(4x)}

解

導関数

4 2 x^{12} + sin (4 x)

\frac{6 x ^{11} + cos ( 4 x )}{( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}}

解答ステップ

\frac{d}{d x} (4 2 x^{12} + sin (4 x))

連鎖法則を適用:

\frac{1}{4 ( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}} \frac{d}{d x} (2 x^{12} + sin (4 x))

= \frac{1}{4 ( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}} \frac{d}{d x} (2 x^{12} + sin (4 x))

\frac{d}{d x} (2 x^{12} + sin (4 x)) = 24 x^{11} + cos (4 x) \cdot 4

= \frac{1}{4 ( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}} (24 x^{11} + cos (4 x) \cdot 4)

簡素化

\frac{1}{4 ( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}} (24 x^{11} + cos (4 x) \cdot 4) : \frac{6 x ^{11} + cos ( 4 x )}{( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}}

= \frac{6 x ^{11} + cos ( 4 x )}{( 2 x ^{12} + sin ( 4 x ) ) ^{\frac{3}{4}}}