What is (\partial)/(\partial t)(arctan(xsqrt(t))) ?

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial t} (x t) = \frac{x}{2 t}

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

Simplify

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

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

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6 x - 8 y x^{2} + 1 \frac{d y}{d x} = 0

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\frac{d}{d x} (20 x^{\frac{1}{2}} - \frac{1}{2} x^{20})

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