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Determine the derivative of each of the following:

a. $y=2 e^{x^{3}}$

b. $y=x e^{3 x}$

c. $f(x)=\frac{e^{-x^{3}}}{x}$

d. $f(x)=\sqrt{x} e^{x}$

e. $h(t)=e t^{2}+3 e^{-t}$

f. $g(t)=\frac{e^{2 t}}{1+e^{2 t}}$

a. $6 x^{2} e^{x^{3}}$

b. $e^{3 x}(3 x+1)$

c. $\frac{-3 x^{2} e^{-x^{3}}(x)-e^{-x^{3}}}{x^{2}}$

d. $\sqrt{x} e^{x}+e^{x}\left(\frac{1}{2 \sqrt{x}}\right)$

e. $2 t e^{\prime^{2}}-3 e^{-t}$

f. $\frac{2 e^{2 t}}{\left(1+e^{2 t}\right)^{2}}$

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{'transcript': "Okay, so we see No, have thought to turn here. So it's take the derivative and use our product role. It's a derivative of E that's negative each evening of X times, the square root of and in plus the derivative of square root of X. So that's 1/2 exit are thinking of 1/2 and in each of the *** vex. So this is our following devoted."}

University of California, Berkeley

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