Differentiation using the first principle is defined as the limit of the difference quotient, specifically expressed as \( f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \). In the case of the function \( y = x^2 + 2 \), applying this definition leads to the derivative \( \frac{dy}{dx} = 2x \). Key steps include expanding the numerator and simplifying the expression. A foundational understanding of basic algebra and limits is essential for mastering this concept.
PREREQUISITESStudents in calculus courses, educators teaching differentiation, and anyone seeking to strengthen their understanding of the first principle of differentiation.
Mathkid12 said:thanks can you please relate it to the question that i provided please, and thanks in advance
Fernando Revilla has given you the first two steps. The next step should be clear: Expand the numerator and simplify. Then ...Mathkid12 said:well i really don't know because I PRESENTLY DONT KNOW ANYTHING ABOUT Differentiation using first principle but thanks anywhere
Then my question would be why are you asking this question? Aren't you taking a Calculus class? Do you know how to take a limit? Do you know how to square a binomial?Mathkid12 said:well i really don't know because I PRESENTLY DONT KNOW ANYTHING ABOUT Differentiation using first principle but thanks anywhere