If y=e^(√2x) then dy/dx is equal to?

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Answer 1 · 2018-03-09T07:07:40

#color(red)(dy/dx=e^(sqrt(2x))sqrt(2x)/(2x))#

.

#y=e^(sqrt(2x))#

Let #u=sqrt(2x)#, and #z=2x#

#(dz)/dx=2#

#u=sqrtz#

#(du)/dz=1/2z^(-1/2)=1/(2sqrtz)=sqrtz/(2z)#

#y=e^u#

#dy/(du)=e^u#

#dy/dx=(dy/(du))((du)/(dz))((dz)/dx)#

#dy/dx=(e^u)(sqrtz/(2z))(2)#

Now, we can substitute back for #u# and #z#:

#dy/dx=e^(sqrt(2x))(sqrt(2x))/(2(2x))(2)#

#dy/dx=e^(sqrt(2x))sqrt(2x)/(2x)#