Find the derivative of function y = x ^ 2-2x + 1 (detailed process orz)

Find the derivative of function y = x ^ 2-2x + 1 (detailed process orz)

y'=(x^2-2x+1)
=(x ^ 2) '- (2x)' + 1 '(derivation addition formula)
=2x-2+0
=2x-2

Find the derivative y 'of function y = x / (x ^ 2 + 4) (detailed process orz)

y'=[(x^2+4)-x(2x)]/(x^2+4)^2=(4-x^2)/(x^2+4)^2

Finding monotone interval y = x of function by derivative method ³+ Ax (a is constant)

y=x ³+ axy'=3x ²+ a①a≥03x ²+ A ≥ 0 ‡ the original function monotonically increases on R ② a < 03x ²+ a=0x ²=- A / 3 ‡ x = ±√ (- A / 3) ‡ y 'in (- ∞, - √ (- A / 3)) and (√ (- A / 3), + ∞) > 0 in (- √ (- A / 3), √ (- A / 3)) < 0 ‡ of the original function

How to find the derivative of F (x) = (1 + x) / (1-x) e ^ (- ax)? Write in detail~

f(x)=(1+x)/(1-x)e^(-ax)
f'(x)='
For typing convenience, set = x1
=x2
=(x1)'(x2)+(x1）（x2)' ...（1）
'=2/(1-x)^2...（2）
'=ae^ax.（3）
Then bring it to (2), (3) and (1)

If the derivative of function f (x) is f '(x) = - x (x + 1), then function g (x) = f (AX-1). (a)

f‘(x)=-x(x+1)
g'(x)=af'(ax-1)=-a(ax-1)(ax-1+1)=-a^2x(ax-1)=-a^3x(x-1/a)
Because a

Find the derivative of y = - x ^ 3 + ax For example, y = - x ^ 3 + the reciprocal of ax

y'=3x^2+a