Question

помогите решить пожалуйста

Answer 1

y=(1+x²)/(2√(1+2x²))
y'(x)=((1+x²)'(2√(1+2x²)-(1+x²)(2√(1+2x²)') /(2√(1+2x²))²=(2x*2√(1+2x²) -(1+x²)*2*4x/(2√(1+2x²)) ) / (4+8x²)=(4x√(1+2x²) - (4x+4x³)/(√(1+2x²)) ) / (4+8x²)=
((4x(1+2x²)-4x-4x³)/(√(1+2x²)) ) / (4+8x²) =(4x+8x³-4x-4x³) / ((4+8x²)√(1+2x²))=4x³/((4+8x²)√(1+2x²))=x³/ ( (1+2x²)√(1+2x²) )