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How do you find the derivative of #f(x)=e^(sqrtx)#?

1 Answer

Feb 15, 2018

#d/dx (e^sqrtx) = e^sqrtx/(2sqrtx)#

Explanation:

Using the chain rule:

#d/dx f(y(x)) = (df)/dy xx dy/dx#

with #y=sqrtx#:

#d/dx (e^sqrtx) = (d/dy e^y) (d/dx sqrt x)#

#d/dx (e^sqrtx) = e^y/(2sqrtx)#

#d/dx (e^sqrtx) = e^sqrtx/(2sqrtx)#

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