use differentials to approximate the change in f(x) if x changes from 3 to 3.01 and f(x) = (3x^2-26)^10

Question

derivative: 10(3x^2-26)^9
f(x+ delta x)= 1 + 10(3x^2-26)^9 * 0.01
= 1 + 10(0.01) <-- Substitute 3 for x
= 1 + 0.1
= 1.1

delta y= 1.1 - 1
delta y= 0.1

but 0.1 is incorrect. why so?

Answer 1

derivative is 10(3x^2-26)^9 * (6x)

Answer 2

The Chain Rule- of course! Thank you very much Steve. :-)