Calculus: Chain Rules and Implicit Differentiation

I've actually already done the first 2 problems I'm posting, but I'd like to see how someone else works them out because I'm not sure about my work. Also, I definitely need to see how to work out the last two for I'm also not sure about them. You'll definitely be repped (thanked). :)

1. Use the quotient rule to find the derivative of

-8sin(x)+9/7x^6-7

You do __not__ need to expand out your answer.

2. a)Find the derivative of: 6e-4xcos(9x). [Hint: use product rule and chain rule!]

b) find the equation of the **tangent line** to the curve at x=0. Write your answer in mx+b format.

3. a)Given the equation below, find dydx.

10x^10+8x30y+y^2=19b) find the equation of the **tangent line** to the curve at (1, 1). Write your answer in mx+b format

4. A fence 24 feet tall runs parallel to a tall building at a distance of 6 ft from the building.

/ | |

/ | |

/ | |

/ 24ft| | (bad pic, sorry)

/______|___6ft_|

We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building.

[A] First, find a formula for the length of the ladder in terms of θ. (*Hint: split the ladder into 2 parts.*)

L(theta) = ?

[b] Now, find the derivative, L'(θ).

L'(theta) = ?

[C] Once you find the value of θ that makes L'(θ)=0, substitute that into your original function to find the length of the shortest ladder. (*Give your answer accurate to 5 decimal places.*)

L(theta(min)) is about ____?___ ft