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- To find the differentiation of 1/x^2, follow these steps:
- Express 1/x^2 as a power of x: 1/x^2 = x^(-2).
- Differentiate both sides with respect to x: d/dx (1/x^2) = d/dx (x^(-2)).
- Apply the power rule of derivatives: d/dx (1/x^2) = -2x^(-2-1) = -2/x^312.
Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.Thus, the differentiation/ derivative of 1/x^2 by first principle is -2/x 3.www.imathist.com/derivative-of-1-x2-by-first-principle/Follow the below steps to find the differentiation of 1 divided by x 2. Express 1/x 2 as a power of x 1/x 2 = x -2 Differentiate both sides w.r.t. x d/dx (1/x 2) = d/dx (x -2) Apply the power rule of derivatives d/dx (1/x 2) = d/dx (x -2) = -2x -2-1www.mathstoon.com/derivative-of-1-x2/ - People also ask
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In calculus, the derivative is the rate of change of a function with respect to a variable or the slope of the tangent line at any given point. For example, the derivative of the position of a moving object (y) with respect to time (x) is the velocity.The expression is invalid or we were unable to solve it0Derivative Calculator: Step-by-Step Solutions - Wolfram|Alpha
Wolfram|Alpha is a great calculator for first, second and third derivatives; derivatives at a point; and partial derivatives. Learn what derivatives are and how Wolfram|Alpha calculates them.
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The Derivative Calculator supports solving first, second...., fourth derivatives, as well as implicit differentiation and finding the zeros/roots. You can also get a better visual and understanding …
Wolfram|Alpha Examples: Step-by-Step Derivatives
See how to evaluate derivatives at a given point: derivative of x^2+4x-2 at x=3. d/dt arctan (t) at t = 1. Perform logarithmic differentiation to compute a derivative: first derivative of 1/x^3. …
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Differentiate a function with Step-by-Step Math …
Differentiate each of the following functions: (a) Since f (x) = 5, f is a constant function; hence f ' (x) = 0. (b) With n = 15 in the power rule, f ' (x) = 15x 14. (c) Note that f (x) = x 1/2 . Hence, with n = 1/2 in the power rule, (d) Since f (x) = …
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Oct 3, 2023 · Find the derivative of. Solution. We begin by applying the rule for differentiating the sum of two functions, followed by the rules for differentiating constant multiples of functions and the rule for differentiating powers.
3.3: Differentiation Rules - Mathematics LibreTexts
Aug 17, 2024 · Use the product rule for finding the derivative of a product of functions. Use the quotient rule for finding the derivative of a quotient of functions. Extend the power rule to …
Derivative Rules - Math is Fun
The Derivative tells us the slope of a function at any point. There are rules we can follow to find many derivatives. For example: The slope of a constant value (like 3) is always 0. The slope of …
How do you find the derivative of 1/x^2? Maths Q&A - BYJU'S
As we know that d d x (x n) = n x n-1. So, d d x 1 x 2 = d d x x-2 =-2 (x)-2-1 =-2 (x)-3 =-2 x 3. Hence, the derivative of 1 x 2 is -2 x 3.
How do you find the derivative of 1/x^2? | Socratic
Mar 30, 2015 · To find the derivative of a ratio, apply the formula. D f (x) g(x) = f '(x)g(x) −f (x)g'(x) g2(x) In particular, if f (x) = 1, you have that f '(x) = 0, and the expression becomes. D 1 g(x) = …
Find the Derivative - d/dx 1/(1+x^2) | Mathway
Differentiate using the chain rule, which states that d dx [f (g(x))] d d x [ f ( g ( x))] is f '(g(x))g'(x) f ′ ( g ( x)) g ′ ( x) where f (x) = x−1 f ( x) = x - 1 and g(x) = 1+x2 g ( x) = 1 + x 2. Tap for more …
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Find the Derivative - d/dx (x^2+1)/(x^2-1) | Mathway
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How do you find the derivative of #1/(1+x^2)#? - Socratic
Jul 19, 2016 · Explanation: Two straightforward ways. Method One. Rewrite as (1 +x2)−1 and use the power and chain rules: h'(x) = −(1 +x2)−2 ⋅ 2x = − 2x (1 + x2)2. Method Two. Use the …
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Covariant derivative - Wikipedia
The covariant derivative is a generalization of the directional derivative from vector calculus. As with the directional derivative, the covariant derivative is a rule, , which takes as its inputs: (1) …
derivative of 1/(x^2) - Symbolab
x^2: x^{\msquare} \log_{\msquare} \sqrt{\square} \nthroot[\msquare]{\square} \le \ge \frac{\msquare}{\msquare} \cdot \div: x^{\circ} \pi \left(\square\right)^{'} \frac{d}{dx} …
How do you find the derivative of #1/x^2 - Socratic
May 16, 2016 · We will use the power rule, which states that the derivative of xn is nxn−1. We can use the power rule once we write 1 x2 as x−2. Thus, according to the power rule, the …
derivative of 1/(X^2) - Symbolab
Click the 'Go' button to instantly generate the derivative of the input function. The calculator provides detailed step-by-step solutions, facilitating a deeper understanding of the derivative …
2.2: Techniques of differentiation - Mathematics LibreTexts
Oct 3, 2023 · Example \(\PageIndex{1}\): Applying Basic Derivative Rules. Find the derivative of \[f(x)=2x^5+7.\] Solution. We begin by applying the rule for differentiating the sum of two …
derivative of 1/(x^2) - Symbolab
x^2: x^{\msquare} \log_{\msquare} \sqrt{\square} \nthroot[\msquare]{\square} \le \ge \frac{\msquare}{\msquare} \cdot \div: x^{\circ} \pi \left(\square\right)^{'} \frac{d}{dx} …
Implicit Derivative Calculator - Symbolab
The implicit diffrentiation is used to find the derivative of one variable in terms of another without having to solve for the variable. Advanced Math Solutions – Derivative Calculator, Implicit …
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