Найти производную функций: а)y=(5x+1) [latex] ^{6} [/latex] б)y=cos[latex] x^{2} [/latex] [latex] \frac{x}{3} [/latex] в)f(x)=[latex] \sqrt{4-x} [/latex]

a) [latex] f^{'}( \sqrt{ (5x+1)^{6} } ) [/latex] [latex] f^{'}((5x+1)^{6} )* \frac{1}{ 2 \sqrt{(5x+1)^{6}} } [/latex] [latex] f^{'}((5x+1)(5x+1)^{5} )* \frac{3}{ \sqrt{(5x+1)^{6}} } [/latex] [latex] f^{'}(5x)(5x+1)^{5}* \frac{3}{ \sqrt{(5x+1)^{6}} } [/latex] [latex] f^{'}(x)(5x+1)^{5}* \frac{15}{ \sqrt{(5x+1)^{6}} } [/latex] [latex] (5x+1)^{5} * \frac{15}{ \sqrt{(5x+1)^{6}} } [/latex] [latex]15 (5x+1)^{2} [/latex] б) [latex]f^{'}( cos x^{ \frac{2x}{3}} )=- sin x^{ \frac{2x}{3} }* f^{'} (x^{ \frac{2x}{3}})=- sin x^{ \frac{2x}{3} }* f^{'} (e^{ln(x)* \frac{2x}{3} })=[/latex][latex]- sin x^{ \frac{2x}{3} }* f^{'} (ln(x)* \frac{2x}{3} })* e^{ln(x)* \frac{2x}{3} } =[/latex][latex]- sin x^{ \frac{2x}{3} }*e^{ln(x)* \frac{2x}{3} }* (f^{'} (ln(x)* \frac{2x}{3}+ln(x)* f^{'} ( \frac{2x}{3} })) =- [/latex][latex]- sin x^{ \frac{2x}{3} }*e^{ln(x)* \frac{2x}{3} }* ( \frac{2}{3}+ln(x) \frac{3* f^{'}(2x)+0*x}{9} ) =[/latex][latex]- sin x^{ \frac{2x}{3} }*e^{ln(x)* \frac{2x}{3} }* ( \frac{2}{3}+ln(x) \frac{2* f^{'}(x)}{3} ) =[/latex][latex]- sin x^{ \frac{2x}{3} }*( \frac{2}{3}+ \frac{2}{3}ln(x))*e^{ln(x)* \frac{2x}{3} } =[/latex][latex]- ( \frac{2}{3}+ \frac{2}{3}ln(x))*sin x^{ \frac{2x}{3} }*e^{ln(x)* \frac{2x}{3} } =[/latex][latex]- ( \frac{2}{3}+ \frac{2}{3}ln(x))*sin x^{ \frac{2x}{3} }*e^{ln(x)* \frac{2x}{3} } =- \frac{2}{3}(ln(x)+1) * sin x^{x* \frac{2}{3} }*e^{x* \frac{2}{3}*ln(x) }[/latex][latex]=- \frac{2}{3}(ln(x)+1) * x^{x* \frac{2}{3} }*sin^{x* \frac{2}{3}}[/latex] в) [latex] f^{'}( \sqrt{4-x} ) =f^{'}(4-x) \frac{1}{2 \sqrt{4-x} } =f^{'}(-x) \frac{1}{2 \sqrt{4-x} } =-f^{'}(x) \frac{1}{2 \sqrt{4-x} } = \frac{1}{2 \sqrt{4-x} } [/latex]