Find the derivative of (x^2+1) ^3(x-1) ^2.

Here we have to find the derivative of [(x^2+1) ^3]*[(x-1)
^2]

Let’s use the product rule
first.

=> (x^2 +1) ^3 * d/dx(x-1) ^2 + d/dx ((x^2+1)
^3)*(x-1) ^2

Now we use the product rule for the individual
terms

d/dx(x-1) ^2 = 2 (x-1) *1 =
2(x-1)

d/dx (x^2+1) ^3 = 3(x^2+1) ^2 * 2x = 6x(x^2+1)
^2

So we get

(x^2 +1)^3 *
d/dx(x-1) ^2 + d/dx ((x^2+1) ^3)*(x-1) ^2

=> (x^2
+1) ^3 * 2(x-1) + 6x(x^2+1) ^2*(x-1) ^2

Simplifying
now

=> 2(x-1) (x^2+1) ^3 + 6x (x-1) ^2 (x^2+1)
^2

=> 2(x^2 +1) ^2 (x-1) [x^2+1 +
3x(x-1)]

=> 2(x^2 +1) ^2 (x-1) [x^2+1 + 3x^2 –
3x]

=> 2(x^2 +1) ^2 (x-1)
[4x^2-3x+1]

Therefore we finally get 2(x^2
+1) ^2 (x-1) [4x^2-3x+1]