What's the derivative of ${arctan x}^{\frac{1}{2}} - 2 x^{\frac{1}{2}}$ $arctanx^(1/2)-2x^(1/2)$ ?

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What's the derivative of ${arctan x}^{\frac{1}{2}} - 2 x^{\frac{1}{2}}$ $arctanx^(1/2)-2x^(1/2)$ ?

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Answer 1 · 2017-08-29T23:33:50

$\frac{d}{d x} (arctan \sqrt{x} - 2 \sqrt{x}) = - \frac{2 x + 1}{2 (x + 1) \sqrt{x}}$ $d/dx(arctansqrtx-2sqrtx) = -(2x+1)/(2(x+1)sqrtx)$

Explanation:

$d/dx arctanf(x) = (f'(x))/([f(x)]^2+1)$

$therefore d/dxarctansqrtx = (1/(2sqrtx))/(1+x) = 1/(2(x+1)sqrtx)$

$d/dx-2sqrtx = -2d/dx2sqrtx = -2* 1/(2sqrtx) = -1/sqrtx$

$therefore d/dx(arctansqrtx - 2sqrtx) = 1/(2(x+1)sqrtx)-1/sqrtx = 1/(2(x+1)sqrtx) -(2(x+1))/(2(x+1)sqrtx) = (1-2(x+1))/(2(x+1)sqrtx) = -(2x+1)/(2(x+1)sqrtx)$

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What's the derivative of ${arctan x}^{\frac{1}{2}} - 2 x^{\frac{1}{2}}$ $arctanx^(1/2)-2x^(1/2)$ ?

1 Answer

Explanation:

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