How do you derive #y = (x^2+8x+3)/x^(1/2)# using the quotient rule?

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How do you derive #y = (x^2+8x+3)/x^(1/2)# using the quotient rule?

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Answer 1 · 2018-03-11T10:26:48

#(3x^2 + 8x - 3)/(2x^(3/2))#

Explanation:

#=[(x^2 + 8x + 3)'(x^(1/2)) - (x^(1/2))'(x^2 +8x + 3)]/(x^(1/2))^2#
#=[x^(1/2)(2x+8) - 1/2x^(-1/2)(x^2+8x+3)]/x#
#=[2x^(3/2) + 8x^(1/2) - 1/2x^(3/2) - 4x^(1/2) - 3/2x^(-1/2)]/x#
#=[3/2x^(3/2) + 4x^(1/2)-3/2x^(-1/2)]/x#
#=[x^(-1/2)[3/2x^2 + 4x -3/2]]/x#
#=[(3x^2 + 8x + 3)/2]/x^(3/2)#
#=(3x^2 + 8x + 3)/(2x^(3/2))#

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How do you derive #y = (x^2+8x+3)/x^(1/2)# using the quotient rule?

1 Answer

Explanation:

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