How do you find the derivative of #y= (x^2 + 2x + 5) / (x + 1)#?

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Answer 1 · 2016-01-08T19:29:08

by using the Quotient rule.

# y =( x^2 + 2x + 5 )/(x + 1 #

applying the Quotient rule as follows gives :

# dy/dx = ((x + 1 ).d/dx (x^2 + 2x + 5 ) - (x^2 + 2x + 5 ).d/dx (x + 1 ))/(x + 1 )^2 #

# rArr dy/dx =( (x + 1 )(2x + 2 ) - (x^2 + 2x + 5 ). 1)/(x +1 )^2 #

'tidying up ' the numerator gives:

# dy/dx = (2x^2 + 4x + 2 - x^2 - 2x - 5 )/(x + 1 )^2 #

# rArr dy/dx =( x^2 + 2x - 3 )/(x + 1 )^2 #