- #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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SUMMARY
The discussion centers on the application of the power rule in calculus for differentiating functions. Users confirm that the power rule can be applied to the function f(x) = 3x^3 - 2x^2 + x, resulting in the first derivative f'(x) = 3x^2 - 4x + 1. It is clarified that the notation f'(x) indicates a single differentiation, while f''(x) denotes the second derivative. The conversation emphasizes that further differentiation is unnecessary unless explicitly seeking higher-order derivatives.
PREREQUISITES- Understanding of basic calculus concepts, specifically differentiation
- Familiarity with the power rule for derivatives
- Knowledge of Leibniz notation for derivatives
- Ability to differentiate polynomial functions
- Study the application of the power rule in more complex polynomial functions
- Learn about higher-order derivatives and their notations
- Explore the implications of differentiating functions multiple times
- Investigate other differentiation rules, such as the product and quotient rules
Students, educators, and anyone studying calculus who seeks to deepen their understanding of differentiation techniques and notation.
can i use the power rule to get the derivative here?
f ' (x) = 3x^2 - 2(2x^1) + 1
- #2
adjacent
Gold Member
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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
Gold Member
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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
Last edited:
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