Differentiation of complex Powers? ie 2^x^2?

I always have trouble remembering how to differentiate complex powers.

x^2 is easy! Its 2x!

But what happens when you have more powers than that?

What if you have 2^x^2 or 2^x^3^x ???

How do you handle these things?

Differentiation of complex Powers? ie 2^x^2?microsoft office

y = 2^(x2)

log y = (x2) (log 2)

(1/y) (dy/dx) = (2) (log 2) (x)

(dy/dx) = (y) (2) (log 2) (x)

dy/dx = (2^x2)(2) (log 2) (x)

dy/dx = 2^(x2 + 1) (log 2) (x)

Differentiation of complex Powers? ie 2^x^2?opera browser internet explorerThank you for your vote. Report It


consider 2^x^2=y

log 2^x^2=log y

x^2*log 2=log y

(1/y)dy/dx=log 2*(2*x) [log 2 is a constant]

dy/dx=(2^x^2) *(log 2)(2*x)

this is the ans