Differentiate (x^3-4)÷(2x+3)?

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Answer 1 · 2017-09-10T06:40:33

The derivative is #=(4x^3+9x^2+8)/(2x+3)^2#

We need the derivative of a quotient

#(u/v)'=(u'v-uv')/(v^2)#

Here, we have

#u=x^3-4#, #=>#, #u'=3x^2#

#v=2x+3#, #=>#, #v'=2#

#((x^3-4)/(2x+3))'=(3x^2(2x+3)-2(x^3-4))/(2x+3)^2#

#=(6x^3+9x^2-2x^3+8)/(2x+3)^2#

#=(4x^3+9x^2+8)/(2x+3)^2#