Question

use the logarithmic differentiation:
y = x-sin(x)....i got it to be....
x^(sinx)(sinx/x+lnxcosx)....im not sure if thats right...

Answer 1

Why would you ever be asked to do that with logarithmic?

Answer 2

thats what the assignments ask

Answer 3

which i have to derviative

Answer 4

Logarithmic just makes that complicated. Its supposed to simplify complicated stuff.
You could do:
ln(y)=ln(x-sin(x))
y'/y=(1-cos(x))/(x-sin(x))
y'=y((1-cos(x))/(x-sin(x))
Replacing y. You are left with just
y'=1-cos(x)

Answer 5

is it
\[x^{-\sin(x)}\]?

Answer 6

its \[y=x ^{sinx}\]

Answer 7

i got it to be \[y=x ^{sinx}(sinx/x+lnxcosx)....\]

Answer 8

AHHHHH lol.
ln(y)=sin(x)ln(x)
y'/y=cos(x)ln(x)+sin(x)/x
y'=y(cos(x)ln(x)+sin(x)/x)
y'=x^(sin(x))(cos(x)ln(x)+sin(x)/x)

Answer 9

but where did i go wrong?

Answer 10

You have the same thing I do. You did it fine, you just do your product rule in a different order :P

Answer 11

o ok...well i guess im getting better

Answer 12

good work!

Answer 13

:D

Answer 14

thanks guys : )