Question

Could anybody show me how to derive by implicit differentiation problem 1F-7b) please ?

Answer 1

We use implicit differentiation when we don't have an explicit formula for the variable we're differentiating. For example, in y=x^2, we have an explicit formula for y, and therefore implicit differentiation does not come into play.

That is the situation in 1F-7b. We have the variable m isolated on the left of the equation, and that is the variable we need isolated because we're looking for dm/dv. Note that m0 on the right side of the equation is a constant, not a variable. We have m isolated on the left side of the equation, so there is no need for implicit differentiation. Or, to put it another way, if we applied the technique of implicit differentiation to this equation, it would be indistinguishable from regular (explicit) differentiation.