What is the derivative of f(x)=ln[x^9(x+3)^6(x^2+7)^5]?

Ronin Daniels

Ronin Daniels

Answered question

2023-03-25

What is the derivative of f ( x ) = ln [ x 9 ( x + 3 ) 6 ( x 2 + 7 ) 5 ] ?

Answer & Explanation

srnessgebf

srnessgebf

Beginner2023-03-26Added 8 answers

Step 1
Use the properties of logarithms to rewrite:
f ( x ) = ln [ x 9 ( x + 3 ) 6 ( x 2 + 7 ) 5 ]
= ln ( x 9 ) + ln ( x + 3 ) 6 + ln ( x 2 + 7 ) 5
= 9 ln ( x ) + 6 ln ( x + 3 ) + 5 ln ( x 2 + 7 )
So,
f ( x ) = 9 x + 6 x + 3 + 5 x 2 + 7 2 x
Simplify algebraically as desired.

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