#### calvin140404

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- Thread starter calvin140404
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How would you find the derivative of y= 3e^(2x) and y = -4e^(11x)? How about y = a*e^(kx) where k is some constant?

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link Step-by-step

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Second, the derivative of a constant, -45, times f is that constant times the derivative of f so that is -45 times the derivative of \(\displaystyle e^{-\frac{ln(90)x}{2}}\).

Third the derivative of e to the f power is e to the f power times the derivative of f so we have \(\displaystyle -45e^{-\frac{ln(90x)}{2}}\) times the derivative of \(\displaystyle \frac{ln(90)x}{2}= \left(\frac{ln(90)}{2}\right)x\).

And that, again, is a constant times x so its derivative is just \(\displaystyle -\frac{ln(90)}{2}\).

So the derivative of \(\displaystyle -45e^{-\frac{ln(90)x}{2}}+ 45\) is

\(\displaystyle (-45)\left(-\frac{ln(90)}{2}\right)e^{-\frac{ln(90)x}{2}}\)