derivative of 6arcsinh(tan(x))

解

\frac{d}{d x} (6 arcsinh (tan (x)))

6 sec (x)

解答ステップ

\frac{d}{d x} (6 arcsinh (tan (x)))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (arcsinh (tan (x)))

連鎖法則を適用:

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

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= 6 \cdot \frac{1}{( tan ( x ) ) ^{2} + 1} sec^{2} (x)

簡素化

6 \cdot \frac{1}{tan ^{2} ( x ) + 1} sec^{2} (x) : 6 sec (x)

= 6 sec (x)