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

Question

Mathematics

Maribel Thomas

9 August, 09:27

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

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Maribel Dean · 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