1. ## derivatives and line tangent help please

Hi, I'm stuck on a couple questions and need major help.

Find f'(x)

*I'm guessing taking derivative in respect of x if that makes any difference..

1. y^2+xy=8
2. sinx+cosy=y^2

Also,

3. Find f'(pi/2) of f(x)=sin(2x)

4. Find d^2y/dx^2 if x^2+y^2=25 at x=4.

5. Find f'(-1) if f(x)=3x^2-4x+9

As for the line tangents... here's the problem I'm stuck with.

6. Find the equation of the line tangent to f(x)=sinx+cosx+1 at x=pi/2.

I started solving it by taking the derivative of f(x)=sinx+cosx+1. But I have no idea what to do next.

Extra problems that I will be extremely grateful for more help...

7. If f(3)=5 and f'(3)=2, what is the best estimate for f(4)
8. At what point on the graph y=3x^2-8x+9 is the tangent line parallel to y=4x+3.

Thank you!!

2. Pblms 1,2, and 4 involve implicit differentiation-- the basic rules are:

1. When diff a fn of x do it normally
2. When diff a fn of y diff wrt to y and multiply by y '

I'll do 1) and leave the other 2 for you

y^2 + xy = 8

2y y ' + y + xy' = 0

y ' (2y +x) = -y

y ' = -y /(2y+x)

3,5, and 8 are fairly simple derivatives you should be able to do them

6 and 7 involve the equation of a tangent line

the formula for a tangent line at (a,f(a)) is

y= f ' (a) (x-a) + f(a)