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2 comments:
Why didn't the 5e^x change when you took the derivative of it?
Here, take the two rules:
- Constant multiple rule.
- Derivative of an exponential function.
The derivative of a function f(x) = e^x is f'(x) = e^x. The derivative is itself.
You are multiplying that function by a constant, in this case "5", and the Constant Multiple Rule says that if the derivative of f(x) is f'(x), then the derivative of cf(x) is cf'(x).
To be practical, some people confuse taking the derivative of a function of the form a^x with the power rule, and think that if:
f(x) = a^x
then
f(x) = a^(x-1)...
THIS IS NOT TRUE. The rule is different because x is in the exponent.
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