Question

y=$frac{5x}{lnx}$ Помогите решить производную

Answer 1

y' = ( 5x/ lnx)' = ( 1/lnx × 5x)'
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Производная произведения:
( u × v)'= u'v + uv'
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( 1/lnx × 5x)' = (1/lnx)'× 5x + (1/lnx) × (5x)'= -1/ln²x × 5x + (1/lnx) × 5 = -5x/ln²x + 5/lnx = ( -5+5lnx)/ ln²x
Ответ: у'= ( -5+5lnx)/ln²x.

Answer 2

y'= [ 5*lnx-5x*1/x ] / ln^2x = [ 5lnx-5 ] / ln^2x