Derivative of Sine: Solutions

$f(x) &sp;=&sp; (3x) sin (x)$
$df dx &sp;=&sp; 3 sin (x) +
(3x) cos (x)$
$f(θ) &sp;=&sp; sin θ θ$
$df dθ &sp;=&sp; θ cos θ - sin θ θ^2^$
$y &sp;=&sp;
3+2 sin (x)$
a) The line $y &sp;=&sp; 2 x - 5$ has a slope of $2$ We want to find the places on the graph of $y &sp;=&sp;
3+2 sin (x)$ that have a derivative of $2$ .
$d dx 3+2 sin (x)
&sp;=&sp; 2 cos (x) &sp;=&sp; 2$ where $x &sp;=&sp
(2n π 23 π$ for all integer values of n.
b) at $x &sp;=&sp; π 6$
$d dx 3+2 sin (x)
&sp;=&sp; 2 cos (x)$
$2 cos (π 6) &sp;=&sp; 3$

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jjnichol@mit.edu