- #1
Danatron
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can i use the power rule to get the derivative here?
f ' (x) = 3x^2 - 2(2x^1) + 1
Can I Use the Power Rule to Get the Derivative Here?
- Thread starter Danatron
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In summary, the power rule can be used to get the derivative of a function. In Leibniz notation, the derivative of a function is represented as f'(x), and the second derivative is represented as f''(x). The derivative of a constant is zero. To differentiate a function twice, we differentiate the function and then differentiate the derivative of the function. This can be extended to differentiate any number of times.
can i use the power rule to get the derivative here?
f ' (x) = 3x^2 - 2(2x^1) + 1
- #2
adjacent
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Of course, why not? Do you use any other rule for that?
Your answer is correct
Your answer is correct
- #3
Danatron
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ok good, so i wouldn't go again until there were no powers?
eg. f ' (x) = 2(3x) - 2(2x) + 1
eg. f ' (x) = 2(3x) - 2(2x) + 1
- #4
adjacent
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No. Why do you have to differentiate it again? The notation ##f'(x)## means-Differentiate once. Similarly, the notation ##f''(x)## means differentiate twice.Danatron said:
In leibniz notations ##\frac{\text{d}}{\text{d}x}## means- Differentiate once and ##\frac{\text{d}^2}{\text{d}x^2}## means- differentiate twice and so on.
In your example,(differentiating twice) you should write ##f''(x)## and this should be equal to the derivative of ##3x^2 - 4x + 1## which is ##6x+4##
Note that the derivative of a constant (1) is zero.
So in general, we differentiate the function ##f##, and again differentiate the derivative of the function ##f##, to differentiate ##f## twice. This can also be extended to differentiating 10000 times
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FAQ: Can I Use the Power Rule to Get the Derivative Here?
What is the power rule for finding derivatives?
The power rule is a method used to find the derivative of a function that is raised to a power. It states that the derivative of x^n is equal to n*x^(n-1), where n is the power.
When should I use the power rule to find a derivative?
The power rule is most commonly used when finding the derivative of a polynomial function, where the variable is raised to a constant power. It can also be used for other types of functions, such as rational functions, by rewriting them in terms of powers.
Can the power rule be used for all types of functions?
No, the power rule can only be used for functions that involve a variable raised to a constant power. It cannot be applied to functions that involve variables in the base or exponent, or functions that involve multiple variables.
What is the process for using the power rule to find a derivative?
The process for using the power rule is to first identify the function and its power, then multiply the power by the coefficient of the variable, and finally, subtract 1 from the power and rewrite the variable with the new power. This will give the derivative of the function.
Are there any exceptions to the power rule?
Yes, there are a few exceptions to the power rule, such as when the power is 0 or 1. When the power is 0, the derivative will always be 0. When the power is 1, the derivative will be equal to the coefficient of the variable. Additionally, the power rule does not apply to functions with negative exponents, logarithmic functions, or trigonometric functions.