Найти производная функции
1) [tex]y=x\cdot ln(x^{2}+1)+ln5[/tex]
2) [tex]y = sin\frac{x}{2}\cdot cos\frac{3x}{2}[/tex]
1) [tex]y=x\cdot ln(x^{2}+1)+ln5[/tex]
2) [tex]y = sin\frac{x}{2}\cdot cos\frac{3x}{2}[/tex]
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Answers & Comments
1) y' = (x*ln(x^2+1)+ln5)'=ln(x^2+1)+x(ln(x^2+1))'= ln(x^2+1)+(2x^2)/(x^2+1)
2) y'=(sin(x/2)*cos(3x/2))'=1/2cos(x/2)*cos(3x/2)-3/2sin(x/2)sin(3x/2)