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
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