What is the derivative of f(x)=5^lnx?

poetinjam4gj4

poetinjam4gj4

Answered question

2023-03-26

What is the derivative of f ( x ) = 5 ln x ?

Answer & Explanation

iistiidgllj

iistiidgllj

Beginner2023-03-27Added 6 answers

Take both sides' natural logarithms.
ln ( f ( x ) ) = ln ( 5 ln x )
Using the following rule, the right side can be made simpler: log ( a b ) = b log ( a )
ln ( f ( x ) ) = ln ( x ) ln ( 5 )
Distinguish the opposing sides. Remember that the left-hand side will employ the chain rule. Remember that ln ( 5 ) is just a constant and will remain on the right-hand side.
1 f ( x ) f ( x ) = 1 x ln ( 5 )
To solve for f'(x), the derivative, multiply both sides by f(x).
f ( x ) = ln ( 5 ) x f ( x )
Rewrite f(x) as 5 ln x .
f ( x ) = 5 ln x ln 5 x

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