Question

Найти производную 1)y=lg(eˣ+5sin3x-4arccosx)
2)y=-$sqrt{ln( x^{3}+4) }+ln sqrt{2x+10}$

Answer 1

$1)quad y=lg(e^{x}+5sin3x-4arccosx)\\y'= frac{e^{x}+15cos3x+frac{4}{sqrt{1-x^2}}}{(e^{x}+5sin3x-4arccosx)ln10} \\2)quad y= sqrt{ln(x^3+4)} +ln sqrt{2x+10} \\y'= frac{1}{2sqrt{ln(x^3+4)}} cdot frac{3x^2}{x^3+4} + frac{1}{ sqrt{2x+10} } cdot frac{2}{2sqrt{2x+10}}$