Question

differentiate using logarithmic differentiation
y=(2(x^2+1))/((cos2x)^(1/2))

Answer 1

take the log of both sides...simplify...differentiate

Answer 2

whoops 2 on the outside because its an exponent

Answer 3

use the log property: lna -lnb=ln a/b

Answer 4

so would it just be the natural log of the top - the natural log of the bottom?

Answer 5

you can simplify more than that

Answer 6

do you mind explaining? i was recently put into calc 2 skipping calc 1 completely, a little confused =/

Answer 7

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

Answer 8

\[\ln(y)=\ln(2)+\ln(x^2+1)-\frac{1}{2}\ln(\cos2x)\]

Answer 9

ohhh alright
makes a lot more sense now! thank you!

Answer 10

now differentiate........1/y dy/dx=0+1/(x^2+1) *2x -1/2 1/cos2x * -2sin2x

Answer 11

back sub your y and multiply it over simplify and your good

Answer 12

thank you!

Answer 13

is the co2x and the -2sin2x both in the denom?
or is the -2sin2x inthe numerator.

Answer 14

\[\frac{1}{\cos(2x)}{(-2\sin(2x))}\]

Answer 15

alright gotcha, thank you