Chain rule on (x²+1)^5 — keep getting 5(x²+1)⁴ and stuck there

The 10x is the derivative of the *inner* function x²+1 — that's 2x — multiplied by the 5 from the power. So 5·2x = 10x, then attach (x²+1)⁴.

What Eunbi said. If you write the composition as g(h(x)) where h(x)=x²+1 and g(u)=u⁵, the chain rule says (g∘h)'(x) = g'(h(x))·h'(x). Try a few more with that explicit substitution — it's worth slowing down on the form.

I had this exact misconception last month — what helped was always writing h(x)= ... on the side before differentiating.