How do you find the derivative of #5^tanx#?

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Answer 1 · 2016-11-30T18:42:28

#d/dx(5^(tan x))=(5^tan x)*ln 5*sec^2 x#

The formula to differentiate is

#d/dx(a^u)=a^u*ln a*d/dx(u)#

therefore

#d/dx(5^tan x)=5^tanx*ln 5*d/dx(tan x)#

#d/dx(5^tan x)=5^tanx*ln 5*sec^2 x*(dx/dx)#

#d/dx(5^(tan x))=(5^tan x)*ln 5*sec^2 x#

God bless....I hope the explanation is useful.