derivative y=sec(sqrt(3x^4+5))

解

導関数

y = sec (3 x^{4} + 5)

\frac{6 x ^{3} sec ( 3 x ^{4} + 5 ) tan ( 3 x ^{4} + 5 )}{3 x ^{4} + 5}

解答ステップ

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

連鎖法則を適用:

sec (3 x^{4} + 5) tan (3 x^{4} + 5) \frac{d}{d x} (3 x^{4} + 5)

= sec (3 x^{4} + 5) tan (3 x^{4} + 5) \frac{d}{d x} (3 x^{4} + 5)

\frac{d}{d x} (3 x^{4} + 5) = \frac{6 x ^{3}}{3 x ^{4} + 5}

= sec (3 x^{4} + 5) tan (3 x^{4} + 5) \frac{6 x ^{3}}{3 x ^{4} + 5}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{6 x ^{3} sec ( 3 x ^{4} + 5 ) tan ( 3 x ^{4} + 5 )}{3 x ^{4} + 5}