What is the derivative of arctan(xsqrt(t)) ?

The derivative of arctan(xsqrt(t)) is (sqrt(t))/(x^2t+1)

What is the first derivative of arctan(xsqrt(t)) ?

The first derivative of arctan(xsqrt(t)) is (sqrt(t))/(x^2t+1)

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

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

Solution steps

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

Treat

t

as a constant

Apply the chain rule:

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

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

\frac{d}{d 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 the derivative of arctan(xsqrt(t)) ?
The derivative of arctan(xsqrt(t)) is (sqrt(t))/(x^2t+1)
What is the first derivative of arctan(xsqrt(t)) ?
The first derivative of arctan(xsqrt(t)) is (sqrt(t))/(x^2t+1)