How do you find the derivative of # 2e^(4x^2)#?

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Answer 1 · 2016-07-23T21:56:26

#f'(x) = 16xe^(4x^2)#

#y = 2e^(4x^2)#

We need to use the chain rule as we have #y(u(x))#.

#(dy)/(dx) = (dy)/(du)(du)/(dx)#

#u = 4x^2 implies (du)/(dx) = 8x#

#(dy)/(du) = d/(du)(2e^u) = 2e^u = 2e^(4x^2)#

Hence

#(dy)/(dx) = 2e^(4x^2)*8x = 16xe^(4x^2)#