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Question #a16fd

1 Answer

May 4, 2016

Use #d/dx(b^x) = b^x lnb# and the chain rule.

Explanation:

#b^x = e^(xlnb)#, so

#d/dx(b^x) = e^(xlnb) * d/dx(xlnb) = e^(xlnb) *lnb = b^x lnb#

For #f(x) = 3^(2x-4)#, apply the previous formula and the chain rule:

#f'(x) = 3^(2x-4) ln3 (d/dx(2x-4)) = 2*3^(2x-4) ln3#

So the exact value of #f'(2)# is #f'(2) = 2ln3#

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