Question

find the second derivative of e^(2x^3)

Answer 1

\[12 e^{2 x^3} \left(x+3 x^4\right) \]

Answer 2

lets say \[y=e^{2x^{3}}\]
then first derivative:
\[y^'=6x^2(e^{2x^{3}})\]
and second derivative: (using product rule)
\[y^''= 6x^2[6x^2(e^{2x^{3}})]+e^{2x^{3}}[12x]\]
simplify, thats your second derivative

Answer 3

\[\int\limits \left(\int\limits 12 e^{2 x^3} \left(x+3 x^4\right)dx\right) \, dx=e^{2 x^3} \]

Answer 4

Thank you guys!!! I have one more question how do u find the second derivative of 3xe^x??

Answer 5

\[3 e^x \text{Log}[e] (2+x \text{Log}[e]) \]

Answer 6

\[\int\limits \left(\int\limits 3 e^x \text{Log}[e] (2+x \text{Log}[e])dx\right) \, dx=3 e^x x \]