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What is the derivative of #5^(x/6)#?

1 Answer

A. S. Adikesavan

May 13, 2016

#=((log 5)/6)5^(x/6)#

Explanation:

Use #a^(kx)=e^(x k log a)# and #(e^(bx))'=be^(bx)#.

#(5^(x/6))'#

#=(e^(((log 5)/6)x))'#

#=((log 5)/6)(e^(((log 5)/6)x))#

#=((log 5)/6)5^(x/6)#

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