How to differentiate #y= (x+2)^2(3x-1)^3# ?

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Answer 1 · 2018-05-29T13:08:10

#dy/dx=(x+2)(3x-1)^2(15x+16)#

#y= (x+2)^2(3x-1)^3#

Differentiate using product rule,

#dy/dx=d/dx[(x+2)^2] (3x-1)^3+d/dx[(3x-1)^3] (x+2)^2#

Differentiate inner terms,

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

Simplify,

#dy/dx=2(x+2)(3x-1)^3+9(3x-1)^2(x+2)^2#

Factor,

#dy/dx=(x+2)(3x-1)^2[2(3x-1)+9(x+2)]#

Simplify,

#dy/dx=(x+2)(3x-1)^2(15x+16)#