Leery e^(x^3) differentiation

[courteous]

If $\displaystyle y=e^{x^3}$, then $\displaystyle y'=3x^2e^{x^3}$, right? But, doesn't $\displaystyle y=e^{x^3}$ equal $\displaystyle e^{3x}$, whose derivation $\displaystyle y_1'=3e^{3x} \neq y'$? This is odd?

Strong sense that I am 'odd man out' ... :lol:

 

[galactus]

No, they are two different animals.

$\displaystyle (e^{x})^{3}=e^{3x}$

But $\displaystyle e^{x^{3}}\neq e^{3x}$

See the difference?.

 

[courteous]

Indeed. Thank you!