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C4 Exponential Decay question

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Hi, I'm not sure about example (b), I thought the dm/dt where m = 200e^-0.04t would just be 200e^-0.04t since differentiating e^x gives you the e^x.

However it says dm/dt = 200 x (-0.04) x e^-0.04t.

Why is this? Need a quick response, thanks :smile:
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Zacken
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Original post by TheKevinFang
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Hi, I'm not sure about example (b), I thought the dm/dt where m = 200e^-0.04t would just be 200e^-0.04t since differentiating e^x gives you the e^x.

However it says dm/dt = 200 x (-0.04) x e^-0.04t.

Why is this? Need a quick response, thanks :smile:


Differentiating eaxe^{ax} gives you aeaxae^{ax}.

This is a special case of the fact that: ddx(ef(x))=f′(x)ef(x)\displaystyle \frac{d}{dx} \left(e^{f(x)}\right) = f'(x)e^{f(x)}

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