Question
Let $f(x)=e^{k x}$ and $g(x)=e^{-k x} .$ Find(a) $f^{(n)}(x)$(b) $g^{(n)}(x)$
Step 1
The first derivative of $f(x)$ is $f'(x)=k e^{k x}$, the second derivative is $f''(x)=k^2 e^{k x}$, and the third derivative is $f'''(x)=k^3 e^{k x}$. We can see a pattern here, the nth derivative of $f(x)$ is $k^n e^{k x}$. Show more…
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