1. Differentiate w.r.t. x
(a) sin^3 (4 x + 1)
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Step-by-step explanation:
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Using chain rule for differentiation
dxd(sin34x)=dxd{(sin4x)3}
=d(sin4x)d{(sin4x)3}dxd(sin4x)
=3(sin4x)3−1d(4x)d{sin(4x)}dxd(4x)
=3sin24x⋅cos(4x)⋅4dxdx [∵dxdx=1] and [dxd(sinx)=cosx]
=12sin24xcos5x.
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