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!