Question

найдите производную функции

f(x)=(4√x +3)(4√x -3)+2x^2

f(x)=(x^2+5)(x^2-4)+2√x

f(x)=√2x^2-(3x-2)5x+1)-√x

Answer 1

1)

$displaystyle f(x)=(4sqrt{x}+3)(4sqrt{x}-3)+2x^2=16x-9+2x^2\\f`(x)=16+4x$

2)

$displaystyle f(x)=(x^2+5)(x^2-4)+2sqrt{x}=x^4+5x^2-4x^2-20+2 sqrt{x}=\\=x^4+x^2+2sqrt{x}-20\\f`(x)=4x^3+2x+frac{1}{sqrt{x} }$

3)

$displaystyle f(x)=sqrt{2}x^2-(3x-2)(5x+1)- sqrt{x}= sqrt{2}x^2-(15x^2-10x+3x-2)- sqrt{x} =\\=x^2(sqrt{2}-15)+7x+2- sqrt{x} \\f`(x)=2x(sqrt{2}-15)+7- frac{1}{2sqrt{x}}$