What's the derivative of #arctanx^(1/2)-2x^(1/2)#?

1 Answer
Monzur R.
Aug 29, 2017

#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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