How do you use the product rule to find the derivative of $y=sqrt(x)*e^x$ ?

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Answer 1 · 2014-09-22T08:22:20

$y'=(1/{2sqrt{x}}+sqrt{x})e^x$

Let us look at some details.

By rewriting the square-root as the 1/2-power,

$y=sqrt{x}cdot e^x=x^{1/2}cdot e^x$

By Product Rule,

$y'=1/2x^{-1/2}cdot e^x+x^{1/2}cdot e^x$

by rewriting the 1/2-power as the square-root,

$=1/{2sqrt{x}}e^x+sqrt{x}e^x$

by factoring out $e^x$ ,

$=(1/{2sqrt{x}}+sqrt{x})e^x$

How do you use the product rule to find the derivative of y=sqrt(x)*e^xy=sqrt(x)*e^x ?