Find the derivative of COS ^ (- 1) (2-x ^ 2)

Find the derivative of COS ^ (- 1) (2-x ^ 2)

[-2xsin(2-x^2)]／[cos(2-x^2)]^2

(COS (x)) ^ - 2 derivative

-2(cosx)^(-3)(-sinx)
=2sinx(cosx)^(-3)

Let y = √ x ²- 1, then y '' = find the second derivative!

y'=1/(2√(x^2-1))*2x=x/√(x^2-1)
y''=(√(x^2-1)-x*1/(2√(x^2-1))*2x)/(x^2-1)=-1/(x^2-1)^(3/2)

What is the derivative of COS (3-x)? Derivation

cos(3-x)'=-sin(3-x)*(-1)=sin(3-x)

It is known that f (x) is differentiable at x = 1 and the derivative of F (1) is 3. Find the value of H tending to 0, Lim [f (1 + H) - f (1)] / h I know the answer is 3. Can you give me a reason, little brother, stupid

f'(1)=3
∴lim[h→0] [f(1+h)-f(1)]/h=3
This is basically the definition of derivative:
Derivative definition
f'(x)=lim[h→0] [f(x+h)-f(x)]/h
And f '(a) = Lim [h → 0] [f (a + H) - f (a)] / h

Inequality proof AB = 1 proof a ^ 2 + B ^ 2 > = 2 radical 2 (a-b) Product of radical 2 and (a-b)

∵a^2 +b^2 ≥2√2（a - b）
∴（a-b)^2 +2 ≥2√2（a - b）
Let x = A-B, then x ^ 2 - 2 √ 2x + 2 ≥ 0, that is (x - √ 2) ^ 2 ≥ 0
∵ (x - √ 2) ^ 2 ≥ 0 is always true ∵ the original question is proved