How do you find the derivative of #y= e^sqrt(x)# ?

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Answer 1 · 2014-09-24T03:03:27

In this problem we have to use the chain rule.

#y=e^(sqrt(x))=e^(x^(1/2))#, convert the square root to its rational power

Apply the chain rule and begin to simplify

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

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

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

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

Convert the exponents to positive numbers

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

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

Rationalize

#y'=e^(sqrt(x))/(2sqrt(x))*((sqrt(x))/(sqrt(x)))#

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