x^log(to the base 1/x^2)of[x^4]?

If your question is d/dx (x^{log_(x^-2)x^4}) .Then here is your solution

Solution: (x^{log_(x^-2)x^4}) = (x^{(log_xx^4)/log_xx^-2})=(x^(4)/(-2))=(x^-2)

d/dx (x^-2) = -2/x³ -----(ans)

Approved

Hi Speed Racer,

As a^^log_a^X = X, only when a is postive.

But as there are square terms in the index and base, this function will be defined for all x ≠ 1.

So the given expression is x^-2.

Hence the differential = -2/x^3.

Hope this helps.

Regards,

Ashwin (IIT MadraS).

Approved