# Thread: Cos Tan Sin

1. ## Cos Tan Sin

I'm stuck on the last three problems of my homework (Yeah almost done). We are suppose to use to the chain rule to find the derivative dy/dx. Here are the problems :

18) cube root (1 + cscx / x)

19) find dy/dx implicitly given x*siny = ysinx - x + y

20) find the equation of the normal line at x = pie/2 rad
y= sinx + cos 2x

These 3 problems make no sense to me and number 20 i have no clue where to start

2. The first one:

Remember that we can write the cube root as a fracitonal power, so look at it like this:

d/dx (1+(cscx)/x)^(1/3) =

(1/3)(1+(csc[x]/x))^(-2/3) * ((-xcscxcotx - cscx)/x^2)

I think this is right..

The chain rule says you bring the exponent in front, repeat the function, and take it down a power. Then you multiply that by the derivative of the inside, the derivative of the inside you would need to use the quotient rule on (low*derivative of high - high*derivative of low, all over low squared)

Hope this helps, I think it's accurate.

3. I can't remember how to do 19 or 20..it's too late and I'm about to go to bed

But if it helps, in case you forgot (I did until just the other day), a line "normal" to the equation means perpendicular.

Good luck!