Question

Vă rog frumos , sa mă ajutați cu aceasta tema! !!
Promit ca va dau coroana

Answer 1

a)f `(x)=3*2x*(x²+1)
b)f `(x)=2x/(x²+1)
c)f `(x)=(1-x)/(1+x)] `:(1-x)/(1+x)=[-(1+x)-(1-x)]/(1+x)²*(1+x)/(1-x)=
(-1-x-1+x)/(1+x)²*(1+x)/(1-x)=-2/(1+x)*(1-x)=-2/(1-x²)
d)aplici formula √ u(x) `=u `(x)/2√u(x)
f `(x)=(x/(1+x)) `*1/2√(x/(1+x)=
(1+x-x)/(1+x)²*1/2√x/(1+x)=
1/2(1+x)²*√(1+x)/√x=(1/2√x)*(1+x)^(2-1/2)=(1/2√x)*(1+x)^(3/2)
e)f `(x)=e^x²+x*2x*e^x²=e^x²+2x²*e^x²=e^x²*(1+2x²)
f)f `(x)=2x*cos(x²+1)
g)f`(x)=(2x+1)*[-sin(x²+x+1)=-(2x+1)*sin(x²+x+1)
h)f `(x)=(sinx) `/2√sinx)=cosx/2√sinx
i)f `(x)=1*√(x²+1)+x*2x/2√(x²+1)=[√(x²+1)²+x²]/√(x²+1)=(2x²+1)/√(x²+1)
j)
f `(x)=(x*e^x) `/2√x*e^x)=(e^x+x*e^x)/2√x*e^x=e^X(1+x)/2*√x*e^x=
√e^x*(1+x)/√x