# calculus

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prove that
d/dx 4x .√(x + √x) = 6x+5 (x)1/2/√(x + √x)
solution is

d/dx 4x.[x+(x)1/2]1/2 = d/dx 4x.[x+(x)^1/2]^1/2

d/dx 4x.[x+(x)^1/2]^1/2
Product Rule

= 4x[1/2(x+(x)^1/2)^-1/2 * (1+1/2x^-1/2) +[x+(x)^1/2]^1/2*4

d/dx(4 x sqrt(x+sqrt(x))) = (2 (1/(2 sqrt(x))+1) x)/sqrt(x+sqrt(x))+4 sqrt(x+sqrt(x))
am i write?

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