How do you find the derivative of $cos(1-2x)^2$ ?

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Answer 1 · 2016-01-13T16:11:20

$4(1-2x)sin(1-2x^2$

Use the chain rule multiple times.

The first issue is the cosine function.

The chain rule states that $d/dx[cos(u)]=-sin(u)*u'$

$d/dx[cos(1-2x)^2]=-sin(1-2x)^2*d/dx[(1-2x)^2]$

The second issue is the squared term.

The chain rule states that $d/dx[u^2]=2u*u'$

$d/dx[(1-2x)^2]=2(1-2x)d/dx[1-2x]$

Since $d/dx[1-2x]=-2$ ,

$d/dx[cos(1-2x)^2]=-sin(1-2x)2*2(1-2x)(-2)$

$=4(1-2x)sin(1-2x)^2$

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