- #1
oridniv
- 9
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I have a test tomorrow so I may keep asking questions frequently. For now, why is it that when the derivative of e^x=e^x, the derivative of e^2x doesn't equal e^2x. I've been looking for the rule but can't find it anywhere.
The derivative of ex is ex itself. This means that the slope of the tangent line to ex at any point is equal to the value of ex at that same point.
The derivative of e2x is 2e2x, not e2x. This is because e2x is a composite function, with e2x as the outer function and 2x as the inner function. When we take the derivative of a composite function, we use the chain rule, which introduces a coefficient of the derivative of the inner function.
Yes, the general rule for finding the derivative of ex is simply ex. This is because ex is its own derivative, as mentioned in the answer to the first question.
No, the derivative of ex is always positive. This is because the graph of ex is always increasing, meaning its slope is always positive. Since the derivative represents the slope of the tangent line, it will always be positive.
The derivative of ex is directly related to the function itself, as it is equal to the function. This is a unique property of ex and is not true for most other functions. This relationship allows us to easily solve differential equations involving ex.