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(1)
y= ln(1-2x)
y' = -2/(1-2x)
(2)
y= (3x+1)/√(1-x^2)
y'
= (3x+1) d/dx {1/√(1-x^2) } + [1/√(1-x^2)] d/dx (3x+1)
= (3x+1) [-(1/2)(1-x^2)^(-3/2) .(-2x) ] + [1/√(1-x^2)] (3)
=(3x+1) [x/(1-x^2)^(3/2) ] + 3/√(1-x^2)
=[ x(3x+1) + 3(1-x^2) ]/(1-x^2)^(3/2)
=( 3x^2+ x + 3- 3x^2 )/(1-x^2)^(3/2)
= (x+3)/(1-x^2)^(3/2)
y= ln(1-2x)
y' = -2/(1-2x)
(2)
y= (3x+1)/√(1-x^2)
y'
= (3x+1) d/dx {1/√(1-x^2) } + [1/√(1-x^2)] d/dx (3x+1)
= (3x+1) [-(1/2)(1-x^2)^(-3/2) .(-2x) ] + [1/√(1-x^2)] (3)
=(3x+1) [x/(1-x^2)^(3/2) ] + 3/√(1-x^2)
=[ x(3x+1) + 3(1-x^2) ]/(1-x^2)^(3/2)
=( 3x^2+ x + 3- 3x^2 )/(1-x^2)^(3/2)
= (x+3)/(1-x^2)^(3/2)
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