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## Main Question or Discussion Point

Hi

I have a question about rearranging the following equation (I saw this in a finance book):

If we rearrange and differentiate

[tex]

Z(t;T) = e^{-\int_{t}^{\tau}r(\tau)d\tau}

[/tex]

We get

[tex]

r(T) = -\frac{\partial}{\partial{T}}(\log{Z(t;T)})

[/tex]

My question is: how do we differentiate the exp(-int()) portion? How can we simplify the integral as an exponent?

Thanks!

I have a question about rearranging the following equation (I saw this in a finance book):

If we rearrange and differentiate

[tex]

Z(t;T) = e^{-\int_{t}^{\tau}r(\tau)d\tau}

[/tex]

We get

[tex]

r(T) = -\frac{\partial}{\partial{T}}(\log{Z(t;T)})

[/tex]

My question is: how do we differentiate the exp(-int()) portion? How can we simplify the integral as an exponent?

Thanks!