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

解

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

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

解答ステップ

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

t

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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