Question

Could someone help me and show me the steps on this question? Thanks

Find the derivative:
g(m) = (m^4+2)^2

Answer 1

chain rule -- think of it like composing functions
a(m) = m^2
b(m) = m^4+2
g(m) = a(b(m))
g'(m) = b'(x) * a'(b(x))

so the derivative of the inner function, m^4+2 is 4m^3, that's just the power and constant rules. the derivative of the outer function, m^2 is 2m. then the trick is to fill in the variable in the outer function with the inner function

g'(m) = 4m^3 * 2(m^4+2)
simplify
g'(m) = 8m^3(m^4+2)

Answer 2

Oh okay, thanks a lot!