Question

Differentiate y= ln l 1+t-t^3 l

Answer 1

is there an absolute value inside the natural logarithm?

Answer 2

yes

Answer 3

cool

Answer 4

what do u do?

Answer 5

just 1/ (1+t-t^3)?

Answer 6

no. first u have to find where the polynomial is positive. in the points where the polynomial changes sign the derivative won't exist, because there we shal have corners.

Answer 7

so..i need to sketch a graph?

Answer 8

i would first solve
\[ \large 1+t-t^3=0 \]

Answer 9

the sketch of the graph would help, of course.

Answer 10

solve u mean find derivative?

Answer 11

but my book has a rules that d/dx lnlxl = 1/x

Answer 12

then all u have missing is the chain rule

Answer 13

by the way. what book is it?

Answer 14

just a remark about what your book says:
if we truly had
\[ \large \frac{d}{dx}\ln|x|=\frac{1}{x} \]
then the slope of the tangent line at \((|-1|,0)=(1,0)\) would be \(m=-1\) so the tangent line would be
\[ \large y=-(x-1) \]

Answer 15

http://www.wolframalpha.com/input/?i=graph+ {y%3Dln+x%2Cy%3D-%28x-1%29}

Answer 16

what do u think?