What is the derivative of # 3^x#?

1 Answer
Jan 4, 2016

Answer:

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

Explanation:

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

To do this, we will use the following:

  1. #ln(a^x) = xln(a)#
  2. The chain rule
  3. #d/dxln(x) = 1/x#
  4. #d/dx cx = c#

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)#