What is the Derivative of y = √x at x = 1?

  • Thread starter Thread starter fiziksfun
  • Start date Start date
  • Tags Tags
    Derivative
AI Thread Summary
To find the derivative of y = √x at x = 1, the limit formula lim x -> a = (f(x) - f(a)) / (x - a) is applied. The expression starts as (√x - 1) / (x - 1), but simplification is needed. A user suggests multiplying by the conjugate (√x + 1) to facilitate simplification. This approach leads to a clearer path for calculating the derivative. The discussion emphasizes the importance of algebraic manipulation in derivative calculations.
fiziksfun
Messages
77
Reaction score
0
I was asked to find the derivative of y=sqrtx at x=1

I need to use the formula

lim x -> a = f(x) - f(a) / (x-a) to find the derivative at x=1

I have..

sqrtx - 1 / (x - 1) BUT i can't simply it from there. Help!

THANKSZ.
 
Mathematics news on Phys.org
Okay:
\frac{\sqrt{x}-1}{x-1}=\frac{\sqrt{x}+1}{\sqrt{x}+1}\frac{\sqrt{x}-1}{x-1}=\frac{(\sqrt{x}+1)(\sqrt{x}-1)}{x-1}\frac{1}{\sqrt{x}+1}
Does that help you a bit?
 

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

B To calculate the polar unit vectors using rotated coordinates
Replies
1
Views
2K
I My attempt to understand horizontal transformations of functions
Replies
6
Views
1K
I Calculating the inverse of a function involving the error function
Replies
3
Views
2K
B How Do You Derive the Formula for sin(x-y)?
Replies
5
Views
2K
I Finding the Largest (or smallest) Value of a Function - given some constant symmetric errors
Replies
3
Views
1K
B Can We Simplify the Taylor Series Expansion for e^(f(x,y))?
Replies
3
Views
2K
B Inverse Functions: Why rewrite as y=f(x) ?
Replies
11
Views
2K
I Formula for the propagation of complex errors
Replies
5
Views
2K
I Question about partial derivative relations for complex numbers
Replies
9
Views
2K
Finding the Derivative of y=sqrt(x+sqrt(x+sqrt(x)))
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top