What is the derivative of #ln(x^2)+5^(2x)#?

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Answer 1 · 2016-10-14T22:09:31

#dy/dx = 2/x + (2ln(5))5^(2x)#

Term-by-term

Term 1:

Before you differentiate use the identity #ln(x^a) = aln(x)#

#2(d[ln(x)])/dx = 2/x#

Term 2:

Use logarithmic differentiation:

#y = 5^(2x)#

#ln(y) = ln(5)2x#

#1/ydy/dx = 2ln(5)#

#dy/dx = (2ln(5))5^(2x)#

Put the two terms back together:

#dy/dx = 2/x + (2ln(5))5^(2x)#