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Problem 3 Easy Difficulty

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

Answer

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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Video Transcript

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