Use the quotient rule to find the derivative?

Question

#f(x)=((4x-1)(3x^2+1))/(5x+2)#

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Answer 1 · 2018-03-08T19:55:47

#d/dx(g(x)/(h(x))) = (g'(x)*h(x) - h'(x)*g(x))/(h^2(x))#

Using the quotient rule,
we get #g(x) = (4x-1)(3x^2+1)# and #h(x) = 5x+2#

#g'(x) = 4(3x^2+1) + 6x(4x-1)#
#h'(x) = 5#

#d/dxf(x) = ((4(3x^2+1) + 6x(4x-1))(5x+2) - 5(4x-1)(3x^2+1))/(5x+2)^2#

#=> (120 x^3 + 57 x^2 - 12 x + 13)/(5 x + 2)^2#