First : you have to draw the hysteresis cycle of the strain vs elongation. Make sure you have closed the cycle.

Second : then take the derivative at any point of the cycle  to have the modulus at that point, or use a math software to get the close equation of the cycle.

As was said above, what is true in linear and nonlinear elasticity is that Young modulus sis the slope of the tangent to the stress-strain relationship at the point.

In nonlinear elasticity, however, you should care about measures of the stress and strain used. The difference between deformed and undeformed configuration matters. Stress and strain are second order tensors and have two indices. By these indices we usually indicate to which configuration they belong, or better say from which they are seen. Used styles are Latin/Greek or Minuscule/Majuscule = Deformed/Undeformed.

Thus we distinguish between Green (or Lagrange) strain tensor with two capital indices and Euler (or Almansi) strain tensor with two small indices. We can also use the deformation gradient – mixed measure with first index small and second capitalized. Measures of the strain are conjugated with the stress measures – Cauchy stress (seen from deformed configuration with both indices small), Second Piloa-Kirchhoff stress with seen in undeformed configuration, or mixed nominal stress).

Elastic modulus, better say a component of the elasticity tensor, obtained by differentiation of the stress with respect to the strain, thus will have four indices – tensor of fourth order. All can be small, capital, or mixed. As I know, no specific names are used to distinguish between them.

It does not matter which you used or prefer. Physical information is still the same. However, every times you should make clear which measure you use by correct indication of indices.

It does matter because mutual transformation of the so-called spatial elasticity tensor (four small indeces) and referential elasticity tensor (four capital indices) involves four times multiplication by the deformation gradient. For instance in the simplest case of uniaxial extension to the stretch equal 2 (twice elongated material), the component of the referential elasticity tensor with four capital indices in the direction of the applied force will be multiplied by 2*2*2*2 when transformed to the totally spatial form.

Take a point 0.2% of Young's modulus. Draw a line parallel to a line starting from the origin having E as the gradient.