Question

Производные элементарных функций. Часть 3

Answer 1

$1.f(x)=2x^3+x^2-3x+3\\f'(x)=6x^2+2x-3\\f'(-2)=6*2^2-4-3=24-4-4=17\\2.f(x)=3^xlog_3x\\f'(x)=(3^x)'log_3x+3^x*(log_3x)'\\f'(x)=3^xln(x)+\frac{3^x}{xln(3)} \\f'(1)=\frac{3}{ln(3)} \\3.f(x)=\frac{x^2-2}{x^2-4}\\f'(x)=\frac{(x^2-2)'(x^2-4)-(x^2-2)(x^2-4)'}{(x^2-4)^2}\\f'(x)=\frac{2x(x^2-4)-2x(x^2-2)}{(x^2-4)^2} \\f'(x)=-\frac{4x}{(x^2-4)^2}\\f'(3) =-\frac{12}{(9-4)^2}\\f'(3)=-\frac{12}{25}$