(\partial)/(\partial x)(arctan(7xsqrt(t)))

解

\frac{\partial}{\partial x} (arctan (7 x t))

\frac{7 t}{49 x ^{2} t + 1}

解答ステップ

\frac{\partial}{\partial x} (arctan (7 x t))

t

を定数として扱う

連鎖法則を適用:

\frac{1}{( 7 x t ) ^{2} + 1} \frac{\partial}{\partial x} (7 x t)

= \frac{1}{( 7 x t ) ^{2} + 1} \frac{\partial}{\partial x} (7 x t)

\frac{\partial}{\partial x} (7 x t) = 7 t

= \frac{1}{( 7 x t ) ^{2} + 1} \cdot 7 t

簡素化

\frac{1}{( 7 x t ) ^{2} + 1} \cdot 7 t : \frac{7 t}{49 x ^{2} t + 1}

= \frac{7 t}{49 x ^{2} t + 1}