How to derivative

1. Dec 18, 2007

innightmare

1. The problem statement, all variables and given/known data

What is the derivative of sin^2(pie*Z) with respect to Z

2. Relevant equations

3. The attempt at a solution

I think the answer is pie/2*sin(pie*Z)

Is this correct? I keep getting confused with whether or not I should involve the 2 or not of should just leaving it along and just focus on my angle, Z

2. Dec 18, 2007

dr3vil704

sin^2(pie*Z) is sin$$^{2}$$($$\pi$$z)?
If it is, Then can't you use the chain rule? which is power rule on the whole out side of the ( ) and then it by multiply by the derivatives of the inside of the ( ). because sin$$^{2}$$($$\pi$$z) is just the same as (sin($$\pi$$z))$$^{2}$$

Last edited: Dec 18, 2007
3. Dec 18, 2007

rocomath

$$(\sin{x})^2 = \sin^{2}x$$

4. Dec 18, 2007

dr3vil704

yeah, so Use the chain rule. Look at it as (sinx)^2 because is easier if you look at it like this.

5. Dec 18, 2007

innightmare

no pie is inside the paranthesis next to Z. I was thinking of doing the chain rule but wasnt sure. but its sin -square and the angle is pie next to Z

Is the answer sin over two *pie

6. Dec 18, 2007

rocomath

$$\frac{d}{dz}\sin^{2}{(\pi Z)}$$

7. Dec 18, 2007

rocomath

no, chain rule?

8. Dec 19, 2007

dr3vil704

hm..I believe the derivative of sin is cos. so the answer should be 2cos(pi*Z) * (Pi) or 2$$\pi$$cos($$\pi$$Z).

the first part is power rule and derivative of the Sin which is Cos. for the inside of the ( ), since it's product of a variable and a constant, we know that Pi is a number hence it a constant. So you take the dervitive of pi*Z and use the product rule:
it will be
Pi*1 + Z*(0)=Pi.

9. Dec 21, 2007

jacobrhcp

no.
chain rule.

>_> just do the derivative of x^2 with respect to x [x=sin(pi z)] (the deravative is 2x). After that multiply by the derivative of x with repect to z. d/dz (sin(pi z)) = pi cos(pi z).

and this is: 2 pi sin(pi z)cos(pi z) and I think thats also equal to pi sin(2pi z) by trigonomtric identities, but not sure about that.

10. Dec 22, 2007

jacobrhcp

never mind this post

11. Dec 22, 2007

NO product rule! $\pi$ is NOT a variable, it is a constant just like 2 or $\frac{3}{4}$ or any other NUMBER.