# Problem with chain rule and product rule

I am having trouble simplifying a problem involving the chain rule and the product rule.

The question is:
Differentiate y=(x-1)^6(x+1)^4

My working is as follow:
dy/dx = (x-1)^6*4(x+1)^3*1+(x+1)^4*6(x-1)^5*1

4(x+1)^3(x-1)^6 + 6(x+1)^4(x-1)^5

This is where I am stuck. The book says the answer is:
2(x-1)^5(x+1)^3(5x+1)

Hi GeoNerd

Good work so far.

When you factorise a4 + a3, you take the lowest power of a out as the common factor, so a4 + a3 = a3(a+1)

dy/dx = 4(x+1)3(x-1)6 + 6(x+1)4(x-1)5

The common factor is (x+1)3(x-1)5

∴ dy/dx = (x+1)3(x-1)5[4(x-1) + 6(x+1)]
∴ dy/dx = (x+1)3(x-1)5[4x-4+6x+6]
∴ dy/dx = (x+1)3(x-1)5(10x+2)
∴ dy/dx = 2(x+1)3(x-1)5(5x+1)

MT