anonymous
  • anonymous
Find the second derivative of f(x)=sinxcosx.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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inkyvoyd
  • inkyvoyd
Well, what's the first derivative?
inkyvoyd
  • inkyvoyd
use the product rule...
saifoo.khan
  • saifoo.khan
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anonymous
  • anonymous
The first derivative is (cosx)^2-(sinx)^2. But how do I take the derivative of that?
inkyvoyd
  • inkyvoyd
well, remember that cos(a+b)=cos a cos b-sin a sin b...
anonymous
  • anonymous
use the chain rule
inkyvoyd
  • inkyvoyd
in other words, use the double angle formula for to reduce the following expression you have obtained. And then use the chain rule.
anonymous
  • anonymous
\[f'(x)=cosx(\cos(x))+(-\sin(x)\sin(x))\] Product Rule and Derivatives of Trigs Simplify. \[f'(x)=\cos ^{2}x-\sin ^{2}x\] \[f''(x)=2\cos(x)(-\sin(x))-2\sin(x)(\cos(x))\] Derivative of Trig and Chain Rule
anonymous
  • anonymous
bring the power down, keep the inside, differentiate inside
inkyvoyd
  • inkyvoyd
Since no one seems to get it USE COS^2 X-SIN^2 X=COS(2x) TO SIMPLIFY EXPRESSION
inkyvoyd
  • inkyvoyd
simplified expression is dy/dx=cos(2x) then take the dervative of that
inkyvoyd
  • inkyvoyd
@Idealist are you followign?
anonymous
  • anonymous
Yes. I got it. Thanks for the help, guys.
inkyvoyd
  • inkyvoyd
I like medals. LOL but yeah, nice to see :) let me know your final answer so I can check it

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