Question

Use logarithmic differentiation to find the derivative of the following equation:
\[\LARGE y= (2x+1)^5(x^4-1)^6\]

Answer 1

don't see how log diff would be used in this.

Answer 2

That's what my stupid online assignment is telling me to use ._.

Answer 3

is there no y = ?
or something atleast..

Answer 4

is this just an expression?

Answer 5

Oh, right

Answer 6

so this is y = ..... right?

Answer 7

Yup~
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Answer 8

Actually, log diff can be useful here.

Answer 9

take the natural log of both sides.
\[\ln y = \ln [(2x+1)^5(x^4-1)^6]\]
now use the log rules..
\[\ln y = \ln (2x+1)^5 + \ln (x^4-1)^6\]

Answer 10

let \[y=\left( 2x+1 \right)^5\left( 5x^4-1 \right)^6\]
\[\ln y=5\ln \left( 2x+1 \right)+6\ln \left(5x^4-1 \right)\]
\[\frac{ y' }{ y }=\frac{ 5*2 }{2x+1 }+\frac{ 6*20x^3 }{5x^4-1 }\]
y'=?
replace the value of y. and get y'

Answer 11

you did pretty much all the work, but ok.

Answer 12

luigi, go review your alg 2

Answer 13

sorry i wrote 5x^4 in place of x^4