The discussion revolves around finding the derivative F'(x) of the function F(x) = √x. The correct approach involves recognizing that the square root can be expressed as a fractional exponent, specifically F(x) = x^(1/2). Consequently, applying the power rule for differentiation, F'(x) = (1/2)x^(-1/2), simplifies to F'(x) = 1/(2√x). Participants emphasized the importance of understanding fractional powers in calculus.
PREREQUISITESStudents studying calculus, particularly those struggling with differentiation of functions involving roots and exponents, as well as educators seeking to clarify these concepts for their students.
The general equation you're after is [tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex]MattsAli1108 said:Homework Statement
F(x)= square root of x
what would F'(x)=?
(F prime of x)
Homework Equations
F(x)= 3x^2
F'(x)=6x
F(x)= x^3
F'(x)=3x^2
The Attempt at a Solution
no clue. If the variable is a square root, it wouldn't have an exponent, right?
confused.