How can I differentiate (sinx) ^x?

Answer 1

If y = (sin(x))^x then ln(y) = x*ln(sin(x)) Now differentiate both sides

(1/y)dy/dx = ln(sin(x)) + x*cos(x)/sin(x) then dy/dx = y{ ln(sin(x)) + x*cos(x)/sin(x) }

but y is just sin(x)^x. Substitute y to get the full answer!