[timgillmoreeztf]

Can someone show me how in the world they did this? MP is the partial derivate , it just stands for marginal product, this is an econ problem.

[Hokimjers]

Partial differentiation is just the same as normal differentiation, you just have to remember that all other variables apart from the one you are differentiating with respect to are held constant.

Basically, the question wants you to do: dy/dx of y = ln(1+x) which you can probably already do.

But just in case:

The above is the same as: y = ln(z) where z = (1+x)

now: dz/dx = 1

therefore: dy/dx = (dy/dz)*(dz/dx) = (1/z)*1 = 1/(1+x)

hence: dy/dx = 1/(1+x)

Having x1 in there, anywhere, won't change the method since it is held constant.

Hope that helps.