Question

differentiate x^-2tan(-7x)

Answer 1

Oo this is a fun one c:

Answer 2

Recall this little trick:\[\Large\rm x=e^{\ln x}\]This helps us when we need to deal with things like:\[\Large\rm x^x=e^{\ln x^x}=e^{x \ln x}\]Then we can differentiate the exponential,
which is a bit easier.

Answer 3

14sec^2(-7x) ln x

Answer 4

\[\Large\rm \color{orangered}{x^{-2\tan(-7x)}}=e^{\ln\left(\color{orangered}{x^{-2\tan(-7x)}}\right)}=e^{-2 \tan(-7x) \ln x}\]This gets it into an easier for to differentiate ^
If this is way confusing, you can instead do your `logarithmic differentiate` the normal way.

Write it as,\[\Large\rm y=x^{-2\tan(-7x)}\]And take log of each side.
That's another way of doing it.