- #1
lioric
- 306
- 20
Plz give me an easy explanation
I do know about the differentiation and second differentiation. I just don't get how that negetive sign comes in front of the exponent in the second differentiation
Differentiation of exponential
- Thread starter lioric
- Start date
In summary, differentiation of exponential refers to finding the rate of change or slope of an exponential function by finding its derivative at a specific point. The derivative is calculated using the power rule and has various applications. It can be negative and indicates the concavity of the function. Some common mistakes when differentiating exponential functions include not using the chain rule, incorrectly applying the power rule, and forgetting to include the natural logarithm. It is important to carefully apply the rules of differentiation to avoid mistakes.
Plz give me an easy explanation
I do know about the differentiation and second differentiation. I just don't get how that negetive sign comes in front of the exponent in the second differentiation
- #2
jedishrfu
Mentor
- 14,785
- 9,123
The "j" represent the imaginary number square-root of minus one. Modern math representations more commonly use "i". However electrical engineering texts will use "j" so as not to confuse the issue of current represented as "i".
https://en.wikipedia.org/wiki/Imaginary_number
Consequently you get the -1 in the second derivative as j*j = -1
https://en.wikipedia.org/wiki/Imaginary_unit
https://en.wikipedia.org/wiki/Imaginary_number
Consequently you get the -1 in the second derivative as j*j = -1
https://en.wikipedia.org/wiki/Imaginary_unit
- #3
lioric
- 306
- 20
Thank you very much
What is the definition of differentiation of exponential?
Differentiation of exponential refers to the process of finding the rate of change or slope of an exponential function. It involves finding the derivative of the function at a specific point.
How is the derivative of an exponential function calculated?
The derivative of an exponential function is calculated using the power rule of differentiation. The general formula is f'(x) = a^x * ln(a), where a is the base of the exponential function.
What is the significance of the derivative of an exponential function?
The derivative of an exponential function is used to find the instantaneous rate of change or slope of the function at a specific point. It is also used in various applications such as population growth, compound interest, and radioactive decay.
Can the derivative of an exponential function be negative?
Yes, the derivative of an exponential function can be negative. This means that the function is decreasing at that particular point. The sign of the derivative also indicates the concavity of the function.
What are some common mistakes made when differentiating exponential functions?
Some common mistakes include forgetting to use the chain rule when the exponential function is nested within another function, incorrectly applying the power rule by only differentiating the base and not the exponent, and forgetting to include the natural logarithm (ln) in the final derivative. It is important to carefully apply the rules of differentiation and check for mistakes when differentiating exponential functions.
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