Question #782a3

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Answer 1 · 2014-11-05T10:25:14

1.) #y=e^{tan(pi t)}#

by differentiating with respect #t#, (Chain Rule)

#=> {dy}/{dt}=e^{tan(pi t)}cdot sec^2(pi t)cdot pi#

by multiplying by #dt#,

#=> dy=pi sec^2(pit)e^{tanpit} dt#

2.) #y=sqrt{7+lnz}=(7+ln z)^{1/2}#

by differentiating with respect to #z#,

#=> {dy}/{dz}=1/2(7+ln z)^{-1/2}cdot1/z=1/{2zsqrt{7+ln z}}#

by multiplying by #dz#,

#=> dy={dz}/{2zsqrt{7+ln z}}#

I hope that this was helpful.