differentiation from first principle

differentiate sqrt(x) from first principles
if y = x sinx , find dy/dx from first principles



differentiate sqrt(x) from first principles
let y =sqrt(x)
first change x to x +
Δx  to get y+Δy
y+Δy=sqrt(x +Δx)
subtract to get
Δy=sqrt(x +Δx)-sqrt(x)
introduce the conjugate on the RHS
divide both sides with
cancel off
Δx on the RHS
and take the limit as

differentiation from first principles
differentiation from first principles

if y = x sinx , find dy/dx from first principles

f(x) = x sinx
f(x+h) = (x+h) sin(x+h)
lim { f(x+h) - f(x)} / h  as h-->0
for that group, simplify  using sinC-sinD formula

Trigonometry formula

use lim (sinh / h ) = 1 as h-->0

differentiation from firstprinciple of xsinx.jpg

other questions and problems:

*integral calculus integration formula

trigonometric identity and ratio of  certain standard angles

*list of differentiation formula     *integral calculus integration formula
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