Question

F(x)=(x+1)^(5)-5x-2 Find F'(x) and zeros of F'(x)

Answer 1

Assuming you mean
$f(x)=(x+1)^5-5x-2$

first use chain rule on first part
derivitive of (x+1)⁵=5(x+1)⁴ times the derivitive of (x+1) which is 1
the first part is 5(x+1)⁴

derivitive of -5x is -5
derivitive of -2 is 0

we gots
f'(x)=5(x+1)⁴-5
find zeroes
0=5(x+1)⁴-5
5=5(x+1)⁴
1=(x+1)⁴
+/-1=x+1
-1+/-1=x
-2=x or 0=x

f'(x)=5(x+1)⁴-5
zeroes at x=-2 and x=0