Question

Найти производную функции

1. (ln (x^2 + 3x + 9))'
2. (8^(3x^2+x+1) )'
3. (3x +5x^2 + x^3) * 4^ x^2
4. log2 (x^3 +3x^2 + 4x +2)'

Answer 1

1) $y'=frac{1}{x^2+3x+9}*(2x+3)=frac{2x+3}{x^2+3x+9}$

2) $y'=8^{3x^2+x+1}*ln(8)*(6x+1)$

3) $y'=(3+10x+3x^2)*4^{x^2}+(3x+5x^2+x^3)*4^{x^2}*ln(4)*2x$

4) $y'=frac{1}{(x^3+3x^2+4x+2)*ln(2)}*(3x^2+6x+4)=frac{3x^2+6x+4}{(x^3+3x^2+4x+2)*ln(2)}$