anonymous
  • anonymous
find the derivative of sin^4 (x)
Mathematics
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anonymous
  • anonymous
find the derivative of sin^4 (x)
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
would it be cos^4x?
anonymous
  • anonymous
i no that the derivative of sin is cos, but the power of 4 confuses me
anonymous
  • anonymous
you can split it up sin^2x * sin^2x than do power reducing

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anonymous
  • anonymous
\[\frac{d}{dx}\sin^2 x=4 \sin ^3 x .\cos x\]
anonymous
  • anonymous
sin^4 x sorry
anonymous
  • anonymous
Have you learned about the chain rule yet?
anonymous
  • anonymous
Rewrite it as (cosx)^4
anonymous
  • anonymous
ya i learned the chain rule
anonymous
  • anonymous
Oops (sinx)^4
anonymous
  • anonymous
Just like newone wrote and chain rule it.
anonymous
  • anonymous
so it would be 4sinx^3 * cos?
anonymous
  • anonymous
yes
anonymous
  • anonymous
ok so what happens here is this. you have to use chain rule. soo.... sin^4(x) --> 4sin^3(x)cos(x)
anonymous
  • anonymous
you can even check it out in wolframalpha
anonymous
  • anonymous
so how do i no when to use the chainrule?
myininaya
  • myininaya
when you have a function inside a function
anonymous
  • anonymous
so for this question sin is the inside function and 4 is the outside?
myininaya
  • myininaya
so we have f(g(x))=(sinx)^4 where f(x)=x^4 and g(x)=sinx
anonymous
  • anonymous
ooooo i c!!
myininaya
  • myininaya
the chain rule is this f'(g(x))*g'(x)
anonymous
  • anonymous
ok. think about it like this. when you find derivative of x^2 its 2x. we stop right here becuase we note that x is not in any function. say if we have cos(2x) then we have to use chain rule. becuase x is inside another function. so derivative of cos(2x) = -sin(2x) = so we derivce the function first. and then we note that we have to further derive x. so we derivce 2x = 2. so we get the final answer cos(2x) = -2sin(2x) chain rule states:
anonymous
  • anonymous
thank u guys!
anonymous
  • anonymous
Let \[u = (sin\ x) \rightarrow (sin\ x)^4 = u^4\ and\ du/dx = cos\ x\] Following the chain rule we have \[d/dx(u^4) = d/du(u^4) * du/dx= 4u^3 * (\cos\ x) = 4(\sin\ x)^3(\cos\ x)\]

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