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Find y if:

  • y=tan1(4x)
  • y=sin(tan1x)
  • Solution (a) Let y=tan1u and u=4x. Then dydu=11+u2 and dudx=4. By the Chain Rule, y=dydx=dydududx=11+u24=41+16x2

    (b) Let y=sinu and u=tan1x. Then dydu=cosu and dudx=11+x2. By the Chain Rule, y=dydx=dydududx=cosu11+x2=cos(tan1x)1+x2