What is the derivative of y = cos (3x + 2)?

What is the derivative of y = cos (3x + 2)?

This problem is called a compound function
y=cos﹙3x+2﹚
y'=-3sin(3x+2)

Find the derivative of the following function (1) y = x + SiNx / X (2) y = cos2x / SiNx + cnsx

First question:
y′＝1＋（xcosx－sinx）/x^2.
Second question:
y′＝（－2sinxsin2x－cosxcos2x）/（sinx）^2－sinx.

Derivative of cos2x

This is the derivative of a compound function. There are two layers. The outer layer is the derivative of COS and the inner layer is the derivative of 2x, so
=-Derivative of sin2x * (2x) = - 2sin2x

Find the derivative of y = cos2x-sin3x

solution
y=cos2x-sin3x
y’=(cos2x-sin3x)'
=(cos2x)'-(sin3x)'
=-2sin2x-3cos3x

Quickly find the first and second derivatives of y = x ^ 2 / 1 + x ^ 2

y'=2x/(1+x^2)^2;
y''=(2-6x^2)/(1+x^2)^3

The second derivative of y = (x-1) / (x + 1) ^ 2

y=(x-1)/(x+2) ²
y`=[(x+1) ²- 2(x-1)(x+1)]/(x+1)⁴
y`=(3-x)/(x+1) ³
y``=[-(x+1) ³- 3(3-x)(x+1) ²]/ (x+1)^6=(2x-10)/(x+1)⁴