#color(red)((1)d/(dt)(t^n)=n*t^(n-1))#
#color(red)((2)d/(d theta)(sintheta)=costheta)#
#color(red)((3)d/(d theta)(tan theta)=sec^2 theta)#
We have,
#y=sin^4(tan5x)=[color(blue)(sin(tan5x))]^color(red)(4)#
#(dy)/(dx)=color(red)(4)*[sin(tan5x)]^color(red)(4-1)*d/(dx)color(blue)((sin(tan5x)),to(1)#
#(dy)/(dx)=4[sin(tan5x)]^3color(blue)((coscolor(red)((tan5x))))*d/(dx)color(red)((tan5x)),to(2)#
#(dy)/(dx)=4sin^3(tan5x)cos(tan5x)color(blue)(sec^2(5x))*d/(dx)color(blue)((5x))#,#color(pink)(to(3))#
#(dy)/(dx)=4sin^3(tan5x)(cos(tan5x))sec^2(5x)*5#
#(dy)/(dx)=20sin^3(tan5x)sec^2(5x)cos(tan5x)#
