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[ ] [ ]2(tan-1x)dx
This came in this year's 12th STD CBSE board exam.
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impt maths questions plzz???
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In bond line notation, a single bond is represented by a single line and a double bond by 2 lines and a triple bond by 3 lines. The ends of the line represent a carbon atom. The hydrogen atoms are not represented specifically but the remaining valency of C are all satisfied by hydrogen unless some other atoms like Cl, O etc are specified. Actually I can go on and on about this but if u can tell me which part ur not clear abt, i'll explain that part in detail. Please go ahead and ask me if u dint find this 2 b clear!
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The bond line notation is a method to draw structural formulas of organic compounds where lines represent the chemical bonds and the edges represent implicit carbon atoms.
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Hey the question is not quite clear. If u cud repost it properly..i'll help ya!!
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I hope u got it. If not please come forward and ask any doubt u hav!!
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The Question is:
If y = (sinx)cosx + (cosx)sinx, prove that
dy/dx = (sinx)cox.[cotx.cosx - sinx(log sinx)] + (cosx)sinx.[cosx (log cosx) - sinx.tanx]
The answer is:
Consider u = (sinx)cosx and v = (cosx)sinx
Hence y = u + v
Differentiating with respect to x, we get
dy/dx = du/dx + dv/dx ........(1)
Now consider u = (sinx)cosx
Taking log on both sides, we get
log(u) = log(sinxcosx)
log(u) = cosx.log(sinx)
Differentiating with respect to x, we get
1/u . du/dx = -sinx.log(sinx) + (cosx/sinx).cosx
du/dx = u.[cotx.cosx - sinx.log(sinx)]
du/dx = (sinx)cosx[cotx.cosx - sinx.log(sinx)].......(2)
Now consider v = (cosx)sinx
Taking log on both sides, we get
log(v) = log(cosxsinx)
log(u) = sinx.log(cosx)
Differentiating with respect to x, we get
1/v . dv/dx = cosx.log(cosx) + (sinx/cosx)(-sinx)
dv/dx = v.[cox.log(cosx) - tanx.sinx]
dv/dx = (cosx)sinx[cox.log(cosx) - tanx.sinx]......(3)
Now from (1), we get dy/dx = (2) + (3)
Hence
dy/dx = (sinx)cosx[cotx.cosx - sinx.log(sinx)] + (cosx)sinx[cox.log(cosx) - tanx.sinx]
Hence proved.
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Not quite sure but is the answer 33?
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Aniline would surely give carbylamine test and hence it shud b the best method!!
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I guess it would be best 2 read from NCERT Txt book for CBSE
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