Question

Use logarithmic differentiation find the derivative of this function:
y= (x² +1)² (x² +x+1)³

Answer 1

I did it wrong, but can someone please pinpoint my mistake and explain?

Answer 2

wrong

Answer 3

\[\ln(y)=\ln[(x² +1)^2]+\ln[(x² +x+1)^3]\]

\[=2\ln(x² +1)+3\ln(x² +x+1)\]

now differentiate

Answer 4

Which rule did you apply to get from the first step to the second?

Answer 5

\[\ln(A^r)=r\ln(A)\]

Answer 6

Ohhh okay

Answer 7

@Zarkon

Answer 8

It's still wrong ..... -.-

Answer 9

\[\frac{d}{dx}\left[2\ln(x² +1)+3\ln(x^2+x+1)\right]\]
\[=2\frac{2x}{x^2+1}+3\frac{2x+1}{x^2+x+1}\]

Answer 10

\[\frac{d}{dx}\ln(y)=\frac{y'}{y}\]

Answer 11

After that step i just substitute the y ? :S

Answer 12

\[\frac{y'}{y}=2\frac{2x}{x^2+1}+3\frac{2x+1}{x^2+x+1}\]

\[y'=y\left(2\frac{2x}{x^2+1}+3\frac{2x+1}{x^2+x+1}\right)\]

now replace y by what it is equal to

Answer 13

Can't i expand ?

Answer 14

if you want