Question

Найти производную функции f(x)＝x'2/x'3+3
f（x）＝(x'3+2x)'4
f(x)＝1/（5x+1)'4
f(x)＝√3x＋11
f（x）＝√2x'4+3x-7

Answer 1

$displaystyle f(x)=frac{x^2}{x^3+3};\f'(x)=frac{2x(x^3+3)-x^2*3x^2}{(x^3+3)^2}=frac{6x-x^4}{(x^3+3)^2};$

$displaystyle f(x)=(x^3+2x)^4;\f'(x)=4(x^3+2x)^3*(3x^2+2)$

$displaystyle f(x)=frac{1}{(5x+1)^4};\f'(x)=frac{-4*4}{(5x+1)^5}=frac{-16}{(5x+1)^5}$

$displaystyle f(x)=sqrt{3x+11};\f'(x)=frac{3}{2sqrt{3x+11}}$

$displaystyle f(x)=sqrt{2x^4+3x-7};\f'(x)=frac{8x^3+3}{2sqrt{2x^4+3x-7}}$