How do you find the derivative of $2 e^{4 x^{2}}$ $2e^(4x^2)$ ?

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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

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

How do you find the derivative of 2e^(4x^2)2e4x2 2e^(4x^2)?