If f (x) = the square of sin2x, then f '(x) is equal to the derivative

If f (x) = the square of sin2x, then f '(x) is equal to the derivative

If sin2x is regarded as a whole, then the derivative of the square of sin2x is 2sin2x
If 2x is regarded as a whole, the derivative of sin2x is cos2x
Finally, the derivative of 2x is 2
According to the principle of derivative of composite function, f '(x) = 2sin2x * cos2x * 2 = 2sin4x

Y = (2x + 3)

That is, first open the square y = 4x ^ 2 + 12x + 9, and then take the derivative, which is simple y '= 8x + 12

Find the derivative y = (x + 1) to the 99th power y = 2E to the - x power y = 2xsin (2x + 5)

[(x+1)^(99)]' = 99(x+1)^(98)
[2e^(-x)]' = -2e^(-x)
[2xsin(2x+5)]' = 2sin(2x+5)+2xcos(2x+5)*2 = 2sin(2x+5) + 4xcos(2x+5)

Find the derivatives of y = x * e ^ 2x + 1 and y = e ^ 2x!

The answers to the two questions are the same, y '= e ^ 2x + X * e ^ X
Basic formula: (e ^ x) '= e^
C '= 0, C is a constant
y'=(a*b)'=a*b'+a'*b
e^2x=e^2+e^x
Derivation: y '= (x * e ^ 2x)' = e ^ 2x + X * (e ^ 2x) '= e ^ 2x + X * (e ^ 2 + e ^ x)' = e ^ 2x + X * e ^ x

Derivative y = 3sin (2x + 3) y = ln (sin4x) y = ln (1 + X squared)

1,y=3sin(2x+3)y'=3cos(2x+3)*(2x+3)'=3cos(2x+3)*2=6cos(2x+3)2,y=ln(sin4x)y'=(1/sin4x)*(sn4x)'=(1/sin4x)*cos4x*(4x)'=cot4x*4=4cot4x3,y=ln(1+x²)y'=1/(1+x²)*(1+x²)'=1/(1+x²)*2x=2x/(1+x...

Y = e ＾ x ＾ 2 + 2x?

y'=e^(x²)*(x²)'+2
=2xe^(x²)+2

How to derive the square X of sin

（sin²x）' = 2sinx * cosx = sin2x

How to calculate the derivative of y = (3x2 + 4x + 4) / (x2 + 4 + 1)

The formula for fractional derivation is: (U / V) '= (u'v-uv') / V ^ 2
There seems to be something wrong with the title
y'=[（3x^2+4x+4）/（x^2+4x+1）]'
= [(6x+4)(x^2+4x+1)-(3x^2+4x+4)(2x+4)]/(x^2+4x+1)^2
Then simplify it

Y = sin (x + Π / 3)'s quadratic derivative! The result is sin (π - 3-2x) or sin (2x + 2 / 3 π). Thank you very much!

Answer 2 = 2Sin (x + π / 3) * cos (x + π / 3) = sin (2x + 2 π / 3)
And these two are equivalent. It must be the second one directly, but it can be the first if you want to deform. There are differences between the two formulas

What is the difference between the sum of the squares of y = (SiNx) and the derivation of squares of y = sin (x)

The derivation of the former is 2sinxcosx
The latter derivative is the square of 2xcos (x)