How do you find the derivative of ${sin}^{2} (2 x + 3)$ $sin^2 (2x+3)$ ?

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Answer 1 · 2015-12-20T06:24:30

$4 sin (2 x + 3) cos (2 x + 3)$ $4sin(2x+3)cos(2x+3)$

According to the chain rule:

$f'(x)=2sin(2x+3)d/dx[sin(2x+3)]$

Now, find that derivative.
$d/dx[sin(2x+3)]=cos(2x+3)overbrace(d/dx[2x+3])^(color(red)(=2))=2cos(2x+3)$

Plug this back in.

$f'(x)=4sin(2x+3)cos(2x+3)$

How do you find the derivative of sin^2 (2x+3)sin2(2x+3) sin^2 (2x+3)?