1.
[(2x+5)^4]'
=4*(2x+5)³*(2x+5)'
=4(2x+5)³*2
=8(2x+5)³
2.
[cos(4-3x)]'
=-sin(4-3x)*(4-3x)'
=-sin(4-3x)*(-3)
=3sin(4-3x)
3.
[ln(1+x²)]'
=[1/(1+x²)]*(1+x²)'
=[1/(1+x²)]*2x
=2x/(1+x²)
4.
(sin²x)'
=2*sinx*1
=2sinx
5.
[(sin2x)/x]'
=[x*(sin2x)'-(sin2x)*x']/x²
=[x*cos2x*(2x)'-(sin2x)]/x²
=(2xcos2x-sin2x)/x²
=(2cos2x)/x-(sin2x)/x²