Find dy/dx if y=√1-tanx/√1+tanx

Answer 1

Let a = sqrt(1-Tan(x)), b = sqrt(1+Tan(x)). c = (1+Tan(x))^3/2

dy/dx = -sec^2(x)*{1/(2ab). +. 1/(2ac)}

Answer 2

I will tell you how to do this, but you will need to work out the details for yourself.

First, recognize that the entire fraction can be under the radical sign.

Second, convert the tan to sin/cos.

Now you have to use the chain rule several times.

The first factor in the derivative is 1/(2 * the radical).

Then you have to multiply it by the derivative of the fraction: remember the mnemonic:

downsie d upsie - upsie d downsie/downsie squared.

You will be left with a fraction involving sin 2x.

Good luck. If you still can't get it, send me a message so that I can try to help further.