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Answer 1 · 2018-01-03T16:46:42

#d/dxf(x)=(-3)/(2x^(3/2))+1/sqrtx#

#f(x)=(3+2x)/(sqrtx)#

This can also be written as #->#

#f(x)=3/sqrtx+(2x)/sqrtx#

#f(x)=3/sqrtx+(2*sqrtx*sqrtx)/sqrtx#

#f(x)=3/sqrtx+(2cancel(sqrtx)sqrtx)/cancel(sqrtx)#

#f(x)=3/sqrtx+2sqrtx#

Now you can differentiate both sides with respect to #x#

The power rule is #d/dxx^n=nx^(n-1)#

#d/dxf(x)=d/dx3/sqrtx+d/dx2sqrtx#

#d/dxf(x)=(-3)/(2x^(3/2))+1/sqrtx#