f(x)=(e²ˣ-e⁻²ˣ)/2 Найти f'(x), при х=0 .
f(x)=(e²ˣ-e⁻²ˣ)/2=(1/2)·e²ˣ- (1/2)·e⁻²ˣ
f'(x)=((1/2)·e²ˣ- (1/2)·e⁻²ˣ)'=(1/2)·(2x)'·e²ˣ- (1/2)·(-2x)'·e⁻²ˣ=(2/2)·e²ˣ+(2/2)·e⁻²ˣ=
=1·e²ˣ+1·e⁻²ˣ=e²ˣ+e⁻²ˣ=e²ˣ+1/e²ˣ=(e⁴ˣ+1)/e²ˣ
f'(0)=(e⁴⁽⁰⁾+1)/e²⁽⁰⁾=(1+1)/1=2
f'(x)=1/2 * (e^2x * 2 -e^-2x *(-2) ) = (2e^2x+2e^-2x)/2 = e^2x+e^-2x
