I need to differentiate $(-x^\frac{1}{\delta} -y^\frac{1}{\delta})^\delta$ with respect to $x$ in order to find a more complex derivative. However, online derivative calculators are all giving something different than what I derived (I wanted to make sure mine's right so I checked with them).
I got the derivative $\delta (\frac{-1}{\delta} x^{\frac{1}{\delta}-1}) (-x^\frac{1}{\delta} -y^\frac{1}{\delta})^{\delta-1}$
I derived this by substituting $u = x^\frac{1}{\delta}$ in the usual manner.
However, every online calculator I use gives the following answer (note the -1 in brackets which gives an additional term):
Is anyone able to explain to me why I'm wrong (or why the online calculators are wrong)?