y=ln[ln2(ln3x)] 求导

题目

y=ln[ln2(ln3x)] 求导
还有y=ln(x+根号下1+x2)求导
2和3都是平方与立方的意思

答案

1.y = ln[ln²(ln³x)]
y' = [ln²(ln³x)]'/ln²(ln³x)
= 2ln(ln³x)*[ln(ln³x)]'/ln²(ln³x)
= 2[ln(ln³x)]'/ln(ln³x)
= 2(ln³x)'/[ln(ln³x)*ln³x]
= 6ln²x(lnx)'/[ln(ln³x)*ln³x]
= 6(lnx)'/[ln(ln³x)*lnx]
= 6/[x*lnx*ln(ln³x)]
y = ln[x+ √(1+x²)]
y' = [x+ √(1+x²)]'/[x+ √(1+x²)]
= [1 +√(1+x²)']/[x+ √(1+x²)]
= [1 + (1/2)*(1+x²)'/√(1+x²)]/[x+ √(1+x²)]
= [1 + x/√(1+x²)]/[x+ √(1+x²)]
= {[x + √(1+x²)]/√(1+x²)}/[x+ √(1+x²)]
= 1/√(1+x²)