Differentiate $ e^{-[y/b]^a} $ respect to y?

Question

I would like to ask that, when I do the differentiation $ \frac{\partial }{ \partial y} e^{-[y/b]^a}$, my answer is $a \times e^{-[y/b]^a} \times (-1/b) $. Is this correct? I am not sure whether $(-1/b)$ should be added.

Thank you very much for reading!! Any suggestions are appreciated!

Answer 1

It's not quite correct... $$\frac\partial{\partial y}e^{-(y/b)^a}=e^{-(y/b)^a}×(-a\color{red}{(y/b)^{a-1}})×\frac1b$$

Answer 2

$$\frac {d}{dy} e^{-(y/b)^a}=?$$

Let $$u=-(y/b)^a$$

Then $$\frac {du}{dy} = -a(y/b)^{a-1}(1/b)$$

Therefore your derivative is $$ \frac {d}{dy} e^{-(y/b)^a}=-a(y/b)^{a-1}(1/b)e^{-(y/b)^a}$$