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**Any help is greatly appreciated!!**

**1. Homework Statement**

**1.Differentiate.**

http://www.webassign.net/www16/symImages/8/a/e5af282af9dd30006849e16c0b489b.gif

**2.Find the derivative of the function.**

http://www.webassign.net/www16/symImages/c/8/fd38a158e810bff80a28202fbceb37.gif

**3.Consider the following.**

http://www.webassign.net/www16/symImages/8/a/68e64f2907886f5478f5c03714da01.gif

(a) Find y ' by implicit differentiation.

(b) Solve the equation explicitly for y and differentiate to get y ' in terms of x.

**4.Differentiate.**

http://www.webassign.net/www16/symImages/1/a/d96706921943b5f83c856dd9fda12e.gif

**5.Differentiate**

http://www.webassign.net/www16/symImages/d/d/cc0e49fd81af528239a0b21a0ac5e9.gif

**3. The Attempt at a Solution**

**1.**On this one I started with the Quotient Rule.

y=sinx/1+cosx

y'=cosx(1+cosx)+(sinx)^2/(1+cosx)^2

y'=cosx+(cosx)^2+(sinx)^2/(1+cosx)^2

I type this in:

(cos(x)+cos^2(x)+sin^2(x))/(1+cos^2(x))

It says: "Check the syntax of your response." I've tried putting them like(cos(x))^2 and (cos^2(x)).

**2.**I tried this one with the chain rule.

I converted it:

s(t)=(t^3+3/t^3-3)^1/4

Now the derivative of the inside is what gets me.

s'(t)=1/4(t^3+3/t^3-3)^-3/4*(inside)

The inside derivative ends up equaling zero. I'm stumped. I used the quotient rule. Heres my attempt of the inside derivative=

3t^2(t^3-3)-(t^3+3)3t^2/(t^3-3)^2

The numerator equals zero, so that times the first part is zero, leaving me with zero. I tried zero but it was wrong.

**3.**Alright, differentiate with respect to x right? I started by converting the radicals.

x^1/2+y^1/2=6

Derivative:

1/2x^(-1/2)+1/2y^(-1/2)y'=6

6 is a constant and equals zero, so I moved the x term over, then divided by 1/2y to get y' by it self:

(-.5x^(.5))/(.5y^(-.5))

Wrong. I didnt attempt the second part yet.

**4.**The derivative(so i've read) of e^x, is simply e^x. I converted the radical. Then applied the product rule.

1/2x^(-1/2)*e^x+x^(1/2)*e^x

Wrong. I think I might have not applied the chain rule to the last term. so If you take the derivative of e^x, it should be e^x? But that shouldn't matter because its still e^x. Right?

**5.**I took the 2nd power and applied to the the entire term.

(1-u/1+u)^2

Then used chain rule.

2(1-u/1+u)*(inside derivative)

inside=

-1(1+u)-(1-u)*1/(1+u)^2

-1-u-1+u/(1+u)^2

-2/(1+u)^2

final answer:

2(1-u/1+u)*(-2/(1+u)^2)

Still wrong. I'm not sure. This is what I typed: 2((1-u)/(1+u))*(-2)/(1+u)^2

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