d/dx (x∧a)=
ax∧a-1
To find the derivative of x raised to the power of a, where a is a constant, we can use the chain rule for differentiation as follows:
d/dx (x^a) = d/dx (e^(a*lnx))
Using the chain rule, we have:
d/dx (e^(a*lnx)) = e^(a*lnx) * d/dx (a*lnx)
Now, we can use the derivative of the natural logarithm function and simplify further:
d/dx (e^(a*lnx)) = e^(a*lnx) * a/x
Finally, substituting e^(lnx) = x, we have:
d/dx (x^a) = a*x^(a-1)
Therefore, d/dx (x^a) = a*x^(a-1).
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