求函数的导数？
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(5)
y=lntan(x/2)
y'
= [1/tan(x/2)] [tan(x/2)]'
= [1/tan(x/2)] [sec(x/2)]^2. ( x/2)'
= [1/tan(x/2)] [sec(x/2)]^2. ( 1/2)
=(1/2) { 1/ [sin(x/2).cos(x/2)] }
=1/sinx
(6)
y=ln[x+ √(x^2-a^2)]
y'
={1/[x+ √(x^2-a^2)] } .[x+ √(x^2-a^2)]'
={1/[x+ √(x^2-a^2)] } .[1+ x/√(x^2-a^2)]
=1/√(x^2-a^2)
y=lntan(x/2)
y'
= [1/tan(x/2)] [tan(x/2)]'
= [1/tan(x/2)] [sec(x/2)]^2. ( x/2)'
= [1/tan(x/2)] [sec(x/2)]^2. ( 1/2)
=(1/2) { 1/ [sin(x/2).cos(x/2)] }
=1/sinx
(6)
y=ln[x+ √(x^2-a^2)]
y'
={1/[x+ √(x^2-a^2)] } .[x+ √(x^2-a^2)]'
={1/[x+ √(x^2-a^2)] } .[1+ x/√(x^2-a^2)]
=1/√(x^2-a^2)
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