Qer
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will post my question in a min
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Qer
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i am watching a tutorial on exam solutions . i stuck here in this tutorial he is using a chain rule but why he wrote 7 and 3 . i dont understand this can anyone please explain this to me .
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MR1999
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i am watching a tutorial on exam solutions . i stuck here in this tutorial he is using a chain rule but why he wrote 7 and 3 . i dont understand this can anyone please explain this to me .
You need to apply the chain rule twice. So for  \displaystyle y=4(\tan 3x)^5, let u=3x and  v=\tan u.

Then \displaystyle \frac{dy}{dx} = \frac{dy}{dv}\cdot \frac{dv}{du}\cdot \frac{du}{dx}
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i am watching a tutorial on exam solutions . i stuck here in this tutorial he is using a chain rule but why he wrote 7 and 3 . i dont understand this can anyone please explain this to me .
try and differentiate a trig value with a constant using a substitution it might help
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i am watching a tutorial on exam solutions . i stuck here in this tutorial he is using a chain rule but why he wrote 7 and 3 . i dont understand this can anyone please explain this to me .
This is where you have to use the chain rule twice.

 \frac{d}{dx} [4(tan(3x))^5] = 5 \times4 tan(3x)^4 \times \frac{d}{dx}(tan(3x))
Which I think you understand.

Now you have to use the chain rule again as \frac{d}{dx}(tan(3x)) = 3sec^2(3x)
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Qer
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again get confused

so 4tan^5 (3x)
4[tan 3x]^5

20[sec^2 3x] tan 3x]^4

tell whereto used chain rule now
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Qer
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NotNotBatman
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Desmos
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MR1999
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(Original post by Qer)
again get confused

so 4tan^5 (3x)
4[tan 3x]^5

20[sec^2 3x] tan 3x]^4

tell whereto used chain rule now
Apply chain rule to tan3x
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Qer
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(Original post by Desmos)
Apply chain rule to tan3x
so 4tan^5 (3x)
4[tan 3x]^5

20[sec^2 3x] tan 3x]^4

applying chain rule to [tan3x ]^4= 4(sec^2 3x] [tan3x]^3
like that????
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MR1999
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(Original post by Qer)
so 4tan^5 (3x)
4[tan 3x]^5

20[sec^2 3x] tan 3x]^4

applying chain rule to [tan3x ]^4= 4(sec^2 3x] [tan3x]^3
like that????
No just to  \tan 3x. Let  u = 3x and y=\tan u. Then y'(x) =u'(x) \sec^2 u

When you differentiate a composite function, you must differentiate every function which makes it up, whether it's constant, linear, quadratic, trig, exponential etc.
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