Question #32432

1 Answer
sjc
Dec 11, 2016

#(dy)/(du)=1/2e^(x/2)=1/2sqrt(e^x)#

Explanation:

rewrite the function as a power of #""e#

#y=sqrt(e^x)=(e^x)^(1/2)#

#y=e^(x/2)#

use the chain rule

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

#u=x/2=>(du)/(dx)=1/2#

#y=e^u=>(dy)/(du)=e^u#

#(dy)/(dx)=e^uxx1/2#

tidying up, and substituting back for #" "u#

#(dy)/(du)=1/2e^(x/2)=1/2sqrt(e^x)#

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