Question

Find the derivative of f (x)=(x^2+1)^3 (x^2+2)^6 using chain rule.

Answer 1

hello :
note :( (u(x))^n)' = n(u(x))^n-1 × (u(x))'
f (x)=(x^2+1)^3 (x^2+2)^6
the derivative is : f"(x) = ((x^2+1)^3)' (x^2+2)^6 + (x^2+1)^3 ((x^2+2)^6)'
f'(x) = 3×2x(x^2+1)² (x^2+2)^6 + (x^2+1)^3 (6×2x)(x^2+2)^5