# Where did this term go? - Help with Example Problem

I'm having trouble figuring out how the term below boxed in red was eliminated on the left side of the equation as shown below. I reviewed properties of exponential functions, and still can't understand how this term was cancelled.

1. Homework Statement

Exponential laws

## The Attempt at a Solution

Well e^(a/b) = b root of e^a which is not the case here. I'm not sure how else this term can be written so that it cancels with the tau c below it in the denominator.

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kreil
Gold Member
The important equation is 2.12

The term you're referring to isn't "cancelled", but Eq 2.13 is merely stating that the LHS can be rewritten in terms of the derivative of a product.

$$\frac{d}{dt} \left[ f(t)g(t) \right] = \frac{df}{dt}g(t)+\frac{dg}{dt}f(t)$$
If you take the derivative of that product, using the product rule above, then you recover the terms.
$$\frac{d}{dt} \left[ h(t) e^{t/{\tau_c}} \right] = \frac{dh}{dt} e^{t/{\tau_c}} + h(t) \frac{d}{dt} \left[ e^{t/{\tau_c}} \right]$$