Question

найти производную функции f(x) =5√x+3sin x -x3+4x

Answer 1

$f(x)=5sqrt{x}+3sin(x)-x^3+4x \ \ f'(x)=(5sqrt{x})'+(3sin(x))'-(x^3)'+(4x)'= \ \ =(5(x)^{frac{1}{2}})'+(3sin(x))'-(x^3)'+(4x)'= \ \ =5*frac{1}{2}*x^{(frac{1}{2}-1)}+3*cos(x)-3*x^{3-1}+4*x^{1-1}= \ \ =frac{5}{2}*x^{(-frac{1}{2})}+3cos(x)-3x^{2}+4x^{0}= \ \ =frac{5}{2}*(frac{1}{x})^{(frac{1}{2})}+3cos(x)-3x^{2}+4=frac{5}{2sqrt{x}}+3cos(x)-3x^{2}+4$