#•color(white)(x)d/dx(tan^-1(f(x)))=1/(1+(f(x))^2)xxf'(x)#
#rArrd/dx(tan^-1((4x)/sqrt(1-4x^2)))#
#=1/(1+((4x)/sqrt(1-4x^2))^2)xxd/dx((4x)/sqrt(1-4x^2))#
#=1/(1+(16x^2)/(1-4x^2))xx....#
#=1/((1-4x^2+16x^2)/(1-4x^2))xx....#
#=(1-4x^2)/(1+12x^2)xxd/dx((4x)/sqrt(1-4x^2))#
#"differentiate using "color(blue)"quotient/chain rule"#
#"given "y=(g(x))/(h(x))" then"#
#dy/dx=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larrcolor(blue)"quotient rule"#
#g(x)=4xrArrg'(x)=4#
#h(x)=(1-4x^2)^(1/2)rArrh'(x)=1/2(1-4x^2)^(-1/2)xx(-8x)#
#color(white)(xxxxxxxxxxxxxxxxxx)=-4x(1-4x^2)^(-1/2)#
#rArrd/dx((4x)/sqrt(1-4x^2))#
#=(4(1-4x^2)^(1/2)+16x^2(1-4x^2)^(-1/2))/(1-4x^2)#
#=(4(1-4x^2)^(-1/2)(1-4x^2+4x^2))/(1-4x^2)#
#=4/(1-4x^2)^(3/2)#
#rArrd/dx(tan^-1((4x)/sqrt(1-4x^2))#
#=(1-4x^2)/(1+12x^2)xx4/(1-4x^2)^(3/2)#
#=4/((1+12x^2)(1-4x^2)^(1/2)#
