Differentiating product and squares of logarithms I need help differentiating. I am really confused how to solve with the lnx in the equation. Which of the logarithm rules do I need to use for this equation? y=12 x ln x+12x−6x(ln x)^2+8

Tessa Peters

Tessa Peters

Answered question

2022-10-30

Differentiating product and squares of logarithms
I need help differentiating. I am really confused how to solve with the ln x in the equation. Which of the logarithm rules do I need to use for this equation?
y = 12 x ln x + 12 x 6 x ( ln x ) 2 + 8

Answer & Explanation

Milton Hampton

Milton Hampton

Beginner2022-10-31Added 16 answers

You wouldn't use any of the normal logarithmic rules, you'd instead use the product and chain rule. Namely, you get
d y d x = 12 ln x + 12 x 1 x + 12 6 ( ln x ) 2 6 x 2 ln x 1 x
This simplifies to
d y d x = 24 6 ( ln x ) 2
The product rule states that for a product of function u v, the derivative is given by
d d x u v = u d v + v d u
The chain rule states that for a composition of function f ( g ( x ) ), the derivative is given by
d d x f ( g ( x ) ) = g ( x ) f ( g ( x ) )

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