Question

Помогите пожалуйста сделать задания

Answer 1

1. a) y'=(x^5-3x³+x²-1)'=5x^4-9x²+2x;
б) $y'=( frac{3x-1}{x^2+1} )'= frac{(3x-1)'(x^2+1)-(3x-1)(x^2+1)'}{(x^2+1)^2}= frac{3(x^2+1)-2x(3x-1)}{(x^2+1)^2}= \ = frac{3x^2+3-6x^2+2x}{(x^2+1)^2}= frac{-3x^2+2x+3}{(x^2+1)^2};$
в) $y'=(ln(x^2+2x))'= frac{1}{x^2+2x}*(x^2+2x)'= frac{1}{x^2+2x}*(2x+2)= frac{2x+2}{x^2+2x};$
г) $y'=(xe^x)'=x'e^x+x(e^x)'=e^x+xe^x.$

2. y'=(sin3x-cos3x)'=3cos3x+3sin3x=3(cos3x+sin3x);
y'(3π/4)=3(cos(3*3π/4)+sin(3*3π/4))=3(cos9π/4+sin9π/4)=
=3(cos(2π+π/4)+sin(2π+π/4))=3(cosπ/4+sinπ/4)=3(√2/2+√2/2)=3*2√2/2=
=3*√2=3√2.

3. v=s'=(2+20t-5t²)=20-10t;
v(1)=20-10*1=20-10=10 (м/с).

Answer 2

Спасибо большое