(x + △ x) ^ 1 / 2-x ^ 1 / 2 derivation

This derivation will be more troublesome
I can only take this delta x as a certain value, and the derivative of the constant = 0
y’=1/2（X+△X)^(-1/2)+1-(1/2)X^(-1/2)

How to find the derivative of F (x) = (x2-x-1) e Λ 2

f（x）=（x2-x-1）e^2
f'(x)=(2x-1)*e^2

(1 / E) ^ x derivation how can there be two answers There are 2 formulas: (1) : Formula 1: (e ^ x) '= e ^ x Solution 1: use formula 1 (1 / E) ^ x = e ^ (- x) to take the power of - x as X Calculation result [(1 / E) ^ x] '= [(1 / E) ^ x] (2) : Formula 2: (a ^ x) '= a ^ xlna Solution 2: use formula 2 to treat 1 / E as a constant a [(1 / E) ^ x] '= (1 / E) ^ XLN (1 / E)= -(1/e)^x Which is right

Your method is wrong:
Use formula 1 (1 / E) ^ x = e ^ (- x) to take the - x power as t
The calculation result [(1 / E) ^ t] '= [(1 / E) ^ t] (- 1), where (- 1) is the derivative of t to X
The derivative of (1 / E) ^ x is [(1 / E) ^ (- x)] (- 1) = - (1 / E) ^ x, which is the same as the result of method 2

Derivation 1 / (e ^ x + e ^ (- x))

y =1/(e^x+e^(-x))
y' = -1/(e^x+e^(-x))^2 . d/dx (e^x+e^(-x))
= -[e^x - e^(-x)]/(e^x+e^(-x))^2

How to find the 3x derivative of E

3e^3x

The 3x power of 10 is equal to 125. Find the 1-x power of 10 You'd better improve it and understand it

10^3x=125
(10^x)^3=5^3
10^x=5
So 10 ^ (- x) = 1 / 5
So 10 ^ (1-x) = 10 × 1/5=2

(x + △ x) ^ 1 / 2-x ^ 1 / 2 derivation