5. Calculus

First Principles Differentiation — Quiz

Test your understanding of first principles differentiation with 5 practice questions.

Practice Questions

Question 1

What does differentiation from first principles find for a function at a point?

Question 2

Which expression is the standard first principles definition of the derivative of $f(x)$ at $x$?

Question 3

Using first principles, what is the derivative of $f(x)=x^2$?

Question 4

For a function $f$, what does it mean if $\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$ does not exist at a point?

Question 5

What is the derivative of a constant function $f(x)=c$ using first principles?