What is the Derivative of 1-e^2x?

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In summary, the derivative of 1-e^2x is -2e^2x. To find the derivative, the power rule and chain rule can be used. The significance of the derivative is that it represents the instantaneous rate of change and can be used to find the slope of the tangent line. The derivative cannot be simplified further, but can be rewritten in different forms.
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erjkism
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derivative of 1-e^2x?

does anyone know how to do this one?

derivative of 1-e^2x?
 
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All that's needed is the chain rule.

Let u = 2x, then u' = 2

y = 1-eu

y' = -euu' = -2e2x
 
  • #3


To find the derivative of 1-e^2x, we can use the power rule and the chain rule. First, we rewrite the expression as 1-e^(2x), where 1 is a constant and e^(2x) is the inner function. Then, using the chain rule, we multiply the derivative of the inner function (2e^(2x)) by the derivative of the outer function (1), giving us a final answer of -2e^(2x). This can also be written as -2(1-e^(2x)).
 

FAQ: What is the Derivative of 1-e^2x?

What is the derivative of 1-e^2x?

The derivative of 1-e^2x is -2e^2x.

How do you find the derivative of 1-e^2x?

To find the derivative of 1-e^2x, you can use the power rule and the chain rule. First, take the derivative of e^2x, which is 2e^2x. Then, multiply it by the derivative of the inner function, which is -2. This gives you the final result of -2e^2x.

Why is the derivative of 1-e^2x equal to -2e^2x?

The derivative of 1-e^2x is equal to -2e^2x because when taking the derivative of e^2x, the constant 2 is brought down as a coefficient, and the negative sign from the 1 is also carried over. This results in the final answer of -2e^2x.

What is the significance of the derivative of 1-e^2x?

The derivative of 1-e^2x represents the instantaneous rate of change of the original function at any given point. It tells us how the function is changing at that specific point, and can be used to find the slope of the tangent line to the function's graph at that point.

Can the derivative of 1-e^2x be simplified further?

No, the derivative of 1-e^2x cannot be simplified further. It is already in its simplest form, and any further simplification would result in an incorrect answer. However, you can use algebraic manipulation to rewrite the derivative in different forms, such as factoring out -2e^2x.

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