What is (\partial)/(\partial x)(arctan(x*sqrt(t))) ?

The answer to (\partial)/(\partial x)(arctan(x*sqrt(t))) is (sqrt(t))/(x^2t+1)

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

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

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

Solution steps

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

Treat

t

as a constant

Apply the chain rule:

\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

Simplify

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

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

What is (\partial)/(\partial x)(arctan(x*sqrt(t))) ?
The answer to (\partial)/(\partial x)(arctan(x*sqrt(t))) is (sqrt(t))/(x^2t+1)