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Nairaland Mathematics Clinic - Education (259) - Nairaland

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Re: Nairaland Mathematics Clinic by killsmith(m): 8:41pm On May 26
tannyp:
.thanks a lot sir,I'm long done with the exam
Hope the exam was a success?
Re: Nairaland Mathematics Clinic by GMacbeth: 6:15pm On Jun 02
Please help me out on this

Re: Nairaland Mathematics Clinic by MeetDx(m): 11:05am On Jun 04
^^^^

Solution to Q1

If y = tan(2x)
Using chain rule =>
Let's Put u = 2x, then... du/dx = 2
so that y = tanu
and dy/du = sec2u
:. dy/dx = dy/du* du/dx => sec2(2x) * 2
:. The derivative of tan(2x) => y' => d/dx{tan2x} => 2sec2(2x) =>2/cos2(2x)

To show that y' = 2(1 + y2)

Take from the RHS
2(1 + y2) => 2{1 + tan2(2x)}
=> 2{1 + sin2(2x)]/cos2(2x)}
=> 2{cos2(2x) + Sin2(2x)}/ cos2(2x).


Since sin2A + Cos2A = 1,
then => cos2(2x) + Sin2(2x) => 1

:. 2(1 + y2) => 2{1/cos2(2x)} => 2sec2(2x) => y' => LHS
Re: Nairaland Mathematics Clinic by MeetDx(m): 11:32am On Jun 04
GMacbeth:
Please help me out on this


Solution to Q2

y = cot(2x)

Using chain rule
let's put u = 2x

So that du/dx = 2

and y = cotu

:. dy/du = -cosec2u

dy/dx = dy/du * du/dx => -cosec2u * 2
=> -2cosec2u
y'=> -2cosec2(2x)


To show that

y' = -2( 1 + y2)


From RHS =>
substitute y = cot(2x)

=> - 2{ 1 + cot2(2x)}

=> -2{1 + cos2(2x)/sin2(2x)}

=> -2{ sin2(2x) + cos2(2x)}/sin2(2x)


Since Sin2A + Cos2A = 1

sin2(2x) + cos2(2x) = 1


:. -2{ 1/sin2(2x)}

=> -2cosec2(2x)
=> y' => LHS
Re: Nairaland Mathematics Clinic by Blessingposhh: 9:22am On Jun 10
Please sir help me out on this

Re: Nairaland Mathematics Clinic by Ragnarr(m): 7:12am On Jun 11
Please help on this

Re: Nairaland Mathematics Clinic by mathefaro(m): 7:36am On Jun 11
Ragnarr:
Please help on this
we know that
Sin²x + Cos²x = 1
Hence cos²x = 1 - Sin²x
Therefore, the LHS of the equation can become sqrt(Cos²x) = Cos x = RHS
Re: Nairaland Mathematics Clinic by Ragnarr(m): 1:30pm On Jun 11
mathefaro:
we know that
Sin²x + Cos²x = 1
Hence cos²x = 1 - Sin²x
Therefore, the LHS of the equation can become sqrt(Cos²x) = Cos x = RHS
thank u sir

1 Like

Re: Nairaland Mathematics Clinic by cole01: 6:54am On Jun 13
Mathefano
MeetDx
mechanics96
Yusman14
Killsmith
Lapacian
All the bosses in the house, plz I really need to submit this, and I just found this thread out, plz help out

Re: Nairaland Mathematics Clinic by SPLENDID25(m): 6:23pm On Jun 13
Please help me out with these.

Re: Nairaland Mathematics Clinic by Flyingngel(m): 9:53pm On Jun 14
Am grateful for stumbling on a thread like this.
I knw it is not late for me.

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