Miscellaneous

Question 1

Derivative of an inverse function

d/dx ƒ^-1(x) |_x=c

Answer 1

1/ [d/dy ƒ(y)]_y=a

Question 2

Differentials

Answer 2

ƒ(x + ∆x) ≈ ƒ(x) + ƒ’(x)∆x

Question 3

Error in measurement formula

Answer 3

dy = ƒ’(x) dx

Question 4

Vectors

Answer 4

v = xi + yj

speed = |v(t)| = √( (dx/dx)² + (dy/dt²) )

Question 5

Linear Approximations

To approximate ƒ(x) with L(x)

Answer 5

L(x) = ƒ(c) + ƒ’(c) (x–c)

Where c is a value close to x that is easily evaluated.