Question #eb4f3
1 Answer
Oct 7, 2017
Explanation:
First, let's see if we can simplify this expression:
#(sqrtx + 1/x)(x-1/sqrtx)#
#sqrtx(x) - sqrtx(1/sqrtx) + 1/x(x) - 1/x(1/sqrtx)#
#xsqrtx - 1 + 1 - 1/(xsqrtx)#
#xsqrtx - 1/(xsqrtx)#
#x^(3/2) - x^(-3/2)#
Now we have something which is much easier to differentiate using power rule.
#d/dx(x^(3/2)-x^(-3/2))#
#= 3/2x^(1/2) - (-3/2)x^(-5/2)#
#= 3/2sqrtx + 3/2(1/sqrt(x^5))#
#= (3sqrtx)/2 + 3/(2sqrt(x^5))#
Final Answer
