Evaluate the following derivatives. d/(dx)[(2x)^(4x)]

sanuluy 2021-01-19 Answered
Evaluate the following derivatives.
ddx[(2x)4x]
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Expert Answer

lamusesamuset
Answered 2021-01-20 Author has 93 answers
Step 1
Given,
ddx[(2x)4x]
Step 2
Given equation can be written as
ddx[(2x)4x]=2ddx[(x)4x]
We can write x4x as follows
x4x=eln(x4x)
e4xln(x)
Hence
ddx[(2x)4x]=2ddx[e4xln(x)]
We apply the chain rule
ddx[(2x)4x]=2[e4xln(x)]ddx[4xln(x)]
=2[e4xln(x)]4[x×1x+ln(x)]
=2[e4xln(x)][1+ln(x)]
2x4x[1+l(x)]
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