求1/[(t^2+1)^(1/2)]的导数

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求1/[(t^2+1)^(1/2)]的导数

求1/[(t^2+1)^(1/2)]的导数
求1/[(t^2+1)^(1/2)]的导数

求1/[(t^2+1)^(1/2)]的导数
解一:
y = 1/√(t² + 1) = (t² + 1)^(-1/2)
y' = (-1/2)(t² + 1)^(-3/2) • (t² + 1)‘
= (-1/2) • 1/(t² + 1)^(3/2) • (2t)
= -t/(t² + 1)^(3/2)
解二:
y = (t² + 1)^(-1/2)
lny = (-1/2)ln(t² + 1)
y'/y = (-1/2) • (2t)/(t² + 1) = -t/(t² + 1)
y' = -t/(t² + 1) • 1/(t² + 1)^(1/2)
y' = -t/(t² + 1)^(3/2)

y=(t²+1)^(-1/2)
所以y'=(-1/2)*(t²+1)^(-1/2-1)*(t²+1)'
==(-1/2)*(t²+1)^(-1/2-1)*(2t)
=-t/[(t²+1)√(t²+1)]