Question

15. Find dy/dx, if y = (sin x)^x​

Answer 1

Answer:

y=sin(x)^x

taking both side log

logy=logsin(x)^x

differentiate both side with respect to X

dlogy/dx=dlogsin(x).x/dx

a/c to chain rule:

dy/y.dx=logsin(x) + x.dlogsin(x)dx

dy/y.dx=logsin(x) +x{1/sin(x).cos(x)}

dy/dx=y[logsin(x) + x{1/sin(x).cos(x)}]