If r²=x²+y²,x=e^t sin t,y=e^t cos t then dr/dt=

If ‘f’ is differentiable function, f(1)=0, f¹(1)=3/5 and y=f(e^2x)e^x then (dy/dx)_x=0 =

d/dx{sin^-1(3x-4x³)}=

d/dx{Tan^-1(x/1-√1-x²)}=

The derivative of a^xlog x+(x²-1) sin x w.r.t x is

If xy(x+y)=2 then dy/dx=

d/dx{cos^-1√(1+x)/2}=

If a,b,c are the fifth terms of log_e(3/2), log_e(4/3), log_e(6/5) then the ascending order of a,b,c is

If y= {(3x-5)^2/3(x²+1)^3/2/(2x+3)^5/2(3x²-1)^1/3}then dy/dx=

d/dx{Tan^-1(3a²x-x³/a³-3ax²)}=