Diff from first principles

Question 1

How do you lay out a diff from first principles question?

Answer 1

• set y=f(x)
• Step 1 set the coordinates, 1st set (x, f(x)) second set (x+h),f(x+h)
• step 2 use formula booklet and make sure limit is on right hand side
• Step 3 simplify and cancel out the h
• Step 4 as h tends to 0 f(x) tends to derivative.

For cos the same but you subtract sin.

Question 2

How do you prove the derivative of sin

Answer 2

let sin0 = f(x)

Step 2 f’(x) = sin(0+h) - sin0 / h

step 3 expand out the sin(0+h)

step 4 factorise so there is a part that will simplify to zero and a part that will simplify to cos

-step sinh/h tends to 1
cosh-1/h tends to 0

Question 3

WHAT IS AN IMPORTANT PLACE TO START ON DIFF FROM FIRST PRINCIPLES?
eg

Answer 3

Let y=f(x)