This is not actually a homework question but something I saw in a (economics) journal article and have been having trouble getting. It's very simple so I thought I'd post it here.(adsbygoogle = window.adsbygoogle || []).push({});

Define the variable V (implicitly) by:

[itex]V=b + \int^{rV}_{0} rV dF(s) + \int^{\infty}_{rV} s dF(s)[/itex],

where r is a constant and F has support on [0,∞).

Question: Show that [itex]\frac{dV}{db}=\frac{1}{1-rF(rV)}[/itex],

My attempted solution: Differentiate with respect to V and use Leibniz's Rule to get

[itex]1=\frac{db}{dV} + r\cdot rVf(V) - 0 + \int^{rV}_0 r dF(s) + 0 - rVf(V) + 0 = \frac{db}{dV} + r^{2} Vf(V) + rF(rV) - rVf(V)[/itex]

Rearrangement yields

[itex]\frac{dV}{db}=\frac{1}{1-rF(rV)+rVf(V)(1-r)}[/itex]

Notice that my solution has an additional ugly term in the denominator.

Is my solution wrong? Or could perhaps a mistake have been made in the article?

Thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Differentiation under the Integral Sign

**Physics Forums | Science Articles, Homework Help, Discussion**