If a function f(x)f(x)f(x) is defined by the determinant f(x)=det(ln(x)x2exsin(x))f(x) = \det \begin{pmatrix} \ln(x) & x^2 \\ e^x & \sin(x) \end{pmatrix}f(x)=det(ln(x)exx2sin(x)), compute the derivative f′(1)f'(1)f′(1).
2sin(1)−e−22\sin(1) - e - 22sin(1)−e−2
sin(1)−e−2\sin(1) - e - 2sin(1)−e−2
cos(1)−e−3\cos(1) - e - 3cos(1)−e−3
cos(1)−2e−1\cos(1) - 2e - 1cos(1)−2e−1