How do you differentiate $y = {(arctan (x))}^{\frac{1}{2}}$ $y=(arctan(x))^(1/2)$ ?

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How do you differentiate $y = {(arctan (x))}^{\frac{1}{2}}$ $y=(arctan(x))^(1/2)$ ?

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Answer 1 · 2017-11-07T20:26:38

$\frac{d y}{d x} = \frac{1}{2 (1 + x^{2}) {(arctan x)}^{\frac{1}{2}}}$ $dy/dx=1/(2(1+x^2)(arctanx)^(1/2)$

Explanation:

$differentiate using the chain rule$ $"differentiate using the "color(blue)"chain rule"$

$given y = f (g (x)) then$ $"given "y=f(g(x))" then"$

$dy/dx=f'(g(x))xxg'(x)larr"chain rule"$

$rArrdy/dx=1/2(arctanx)^(-1/2)xxd/dx(arctanx)$

$color(white)(rArrdy/dx)=1/2(arctanx)^(-1/2)xx1/(1+x^2)$

$color(white)(rArrdy/dx)=1/(2(1+x^2)(arctanx)^(1/2))$

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How do you differentiate $y = {(arctan (x))}^{\frac{1}{2}}$ $y=(arctan(x))^(1/2)$ ?

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How do you differentiate $y = {(arctan (x))}^{\frac{1}{2}}$ $y=(arctan(x))^(1/2)$ ?