MIT univariate calculus

Question 1

What is the notation for a derivative?

Answer 1

d / dx

also in calculus noted as f’(x)

Question 2

What does it mean to differentiate something?

Answer 2

Find it’s derivative, which is the rate of change or the slope of the tangent line to a point of a function

Question 3

What defines the slope of a tangent line?

What is the slops of the tangent line?

Answer 3

It is equal to the limit of secant lines PQ as Q approaches P (P is fixed).

A secant line is a line that passes through 2 points in a curve

The slope of a tangent line is the limit change in Y divided by the change in X, typically denoted as “m”

Question 4

What is a general formula for the derivative of a function?

Answer 4

Let f(x) is a function whose domain contains an open interval about some point x₀. Then the function f(x) is said to be differentiable at point (x)₀, and the derivative of f(x) at (x)₀ is represented using formula as:

f’(x)= lim_Δx→0 Δy/Δx

⇒ f’(x)= lim_Δx→0 [f((x)₀+Δx)−f((x)₀]/Δx

https://www.cuemath.com/derivative-formula/

Question 5

What is the derivative for f(x) = 1/x ?

Answer 5

derivative = limit of change in Y / change in X as x approaches 0

Δy/Δx = (1/