# Homework Help: 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.