Find the derivative of the following function (1)Y=X^3 (2)Y=2X^2-1 (3)Y^2=X^2+3X

Find the derivative of the following function (1)Y=X^3 (2)Y=2X^2-1 (3)Y^2=X^2+3X

（1）y'=3x^2
(2)y'=4x
(3)2yy'=2x+2
∴±√(x²+3x)y'=x+1
y'=±(x+1)/√(x²+3x)
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About derivative and convex function, concave function problem! What is convex function and concave function? How to judge whether it is convex function or concave function by derivative?

Concave function: Let f (x) be defined on [a, b]. If any two different points in [a, b] x1, X2 hold: F [(x1 + x2) / 2] > = [f (x1) + F (x2)] / 2, then f (x) is said to be concave on [a, b]
Convex function: Let f (x) be defined on [a, b], if any two different points in [a, b] x1, X2 hold: F [(x1 + x2) / 2]

If the second derivative of a function is greater than 0, then the function is concave in this region Right? Wrong?

The second derivative of y = X3 is greater than 0 when x > 0, but it is not concave in this region

Derivation of COS double angle formula Cosine double angle 1.Cos2α=1-2Sinα^2 2.Cos2a=2Cosa^2-1 How did it come out?

Cos2α=cos(α+α)
=cosαcosα-sinαsinα
=cos^2α-sin^2α
=1-sin^2α-sin^2α
=1-2Sinα^2
Cos2α=cos(α+α)
=cosαcosα-sinαsinα
=cos^2α-sin^2α
=cos^2α-(1-cos^2α)
=2cos^2α-1

The formula of double angle is derived

sin2α = sin(α+α) = sinαcosα + cosαsinα= 2sinαcosα
Cosine double angle formula:
The formula of cosine double angle has three groups of expressions, and the three groups are equivalent
　　1.cos2α = 2cos^2 α- 1
　　2.cos2α = 1 − 2sin^2 α
　　3.cos2α = cos^2 α − sin^2 α
deduction:
　　cos2A = cos(A+A) = cosAcosA - sinAsinA = cos^2 A- sin^2 A = 2cos^2 A - 1=1 - 2sin^2 A
Tangent double angle formula:
　　tan2α = 2tanα/[1 - (tanα)^2]
　　tan(1/2*α)=(sin α)/(1+cos α)=(1-cos α)/sin α
deduction:
　　tan(2a) = tan(a+a) = （tan(a) + tan(a)）/（1 - tan(a)*tan(a) ）= 2tanα/[1 - (tanα)^2]

What is the step of deducing the formula of double angle? Sine double angle sin2 α = 2cos α sin α The derivation formula sin2a = sin (a + a) = sinacosa + cosasina = 2sinacosa From sinacosa + cosasina to 2sinacosa, why is there no plus sign? Extract common factor? I also want to give points, but I've run out of them

Sinacosa and cosasina are the same... It's just that the position has changed before and after, and the numerical value is equal, just like AB = Ba, that's what AB + Ba = 2Ab means

How is the double angle formula cos2a derived cos^2（α）－ sin^2（α）= 2cos^2（α）－ 1 Why do we deduce this What is the principle

cos2a=cos(a+a)=cos a*cos a-sin a*sin a=cos^2（α）-(1-cos^2（α）)=2cos^2（α）－ 1

What is the sine of the 72 degree angle

sin72=0.951056516

27 degree angle sine value What is the sine of the 27 degree angle?

Press the calculator
sin27=0.453990499

If angle a = angle B, how can we prove that the sine value of angle a is equal to the sine value of angle B?

For example, an isosceles triangle is the height of the base, and the three lines of the isosceles triangle are collinear, so the sine of the two corners is opposite side / hypotenuse, the oblique side is waist equal, and the opposite side is high. OK