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How do you differentiate #x^sqrt5+sqrt(5x)#?

1 Answer

Nov 25, 2017

# dy/dx=sqrt5*x^(sqrt5-1)+sqrt5/(2sqrtx).#

Explanation:

#d/dx{x^(sqrt5)+sqrt(5x)},#

#=d/dx{x^sqrt5}+d/dx{sqrt5*x^(1/2)},#

#=sqrt5*x^(sqrt5-1)+sqrt5*d/dx{x^(1/2)},#

#=sqrt5*x^(sqrt5-1)+sqrt5{1/2x^((1/2)-1)},#

#=sqrt5*x^(sqrt5-1)+sqrt5{1/2x^(-1/2)}.#

# rArr dy/dx=sqrt5*x^(sqrt5-1)+sqrt5/(2sqrtx).#

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