Y =
x ² In (x)sin (2x)
find derivative please step by step and state which rules are used

Step-by-step explanation:

y=x² ln(x)sin 2x

taking log of both sides

log y=log(x² in(x)sin 2x)=log x²+log.ln (x)+log (sin2 x)

=2log x+log .ln(x)+log sin 2x

diff. w.r.t.x

1/y×(dy/dx)=2/x+(1/ln(x))×(1/x)+( 2 cos 2x/sin2x)

dy/dx=y[2/x+(1/x.ln(x))+2 cot 2x]

dy/dx=x² in(x) sin (2x)[2/x+1/xin(x)+2 cot 2x]

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i