Question

For 0 < x < PI/2, if y = sin(x)^x, then dy/dx is..

I understand that you can take the natural logarithm of both sides and then take the derivative but why can't I simply take the derivative of it and get.. dy/dx = x(cos(x))(sin(x))^(x-1).

Thanks in advance :).

Answer 1

Oh that was silly >.>.. I can't apply the power rule since it doesn't have a constant exponent. So is the only way to differentiate this equation is to use the natural logarithm and then the power + chain rule?

Answer 2

Yes