How do you find the derivative of $(e^{2 x}) \cdot (cos 2 x)$ $(e^(2x)) * (cos 2x)$ ?

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Answer 1 · 2015-12-13T23:08:22

$2 e^{2 x} (cos (2 x) - sin (2 x))$ $2e^(2x)(cos(2x)-sin(2x))$

$f'(x)=cos(2x)d/dx[e^(2x)]+e^(2x)d/dx[cos(2x)]$

Find each derivative independently. They both require use of the chain rule.

$d/dx[e^(2x)]=e^(2x)d/dx[2x]=2e^(2x)$

$d/dx[cos(2x)]=-sin(2x)d/dx[2x]=-2sin(2x)$

Plug these back in.

$f'(x)=2e^(2x)cos(2x)-2e^(2x)sin(2x)$

$f'(x)=2e^(2x)(cos(2x)-sin(2x))$

How do you find the derivative of (e^(2x)) * (cos 2x)(e2x)⋅(cos2x) (e^(2x)) * (cos 2x)?