(\partial)/(\partial x)(arctan(x*sqrt(t)))

解答

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

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

求解步骤

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

将

t

视为常数

使用连锁律:

\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

化简

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

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

l a pl a ce t r an s f or m 2^{t}

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