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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
${d \over {dx}}[{\sin ^n}x\cos \,nx] = $
  • ✓
    $n{\sin ^{n - 1}}x\cos (n + 1)x$
  • B
    $n{\sin ^{n - 1}}x\cos \,nx$
  • C
    $n{\sin ^{n - 1}}x\cos (n - 1)x$
  • D
    $n{\sin ^{n - 1}}x\sin (n + 1)x$
✓

Answer

Correct option: A.
$n{\sin ^{n - 1}}x\cos (n + 1)x$
a
(a) $\frac{d}{{dx}}[{\sin ^n}x\cos nx] = n{\sin ^{n - 1}}x\cos x\cos nx - n\sin nx{\sin ^n}x$

$ = n{\sin ^{n - 1}}x[\cos x\cos nx - \sin nx\sin x] = n{\sin ^{n - 1}}x\cos \,(n + 1)x$.

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