What is the derivative of # 3^x#?

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Answer 1 · 2016-01-04T08:50:14

#d/dx 3^x = 3^xln(3)#

An easy way of doing this is by using logarithmic differentiation.

To do this, we will use the following:

Let #y = 3^x#

#=> ln(y) = ln(3^x) = xln(3)#

#=> d/dxln(y) = d/dxxln(3)#

#=> 1/y dy/dx = ln(3)#

#=> dy/dx = yln(3) = 3^xln(3)#

#:. d/dx 3^x = 3^xln(3)#