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Why is the absolute value function not differentiable at x=0?
Last Updated: 23 July 2025
The absolute value function is not differentiable at x = 0 because the function has a sharp corner at that point, resulting in a discontinuity in the slope of the tangent ...
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When does L' Hopital's Rule Fail?
Last Updated: 23 July 2025
L'Hopital's Rule fails when the limit doesn't result in an indeterminate form like 0/0 or ∞/∞, or when the derivatives involved don't exist or approach infinity.In this ar...
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What is dx in Integration?
Last Updated: 21 August 2025
In integration, dx signifies an infinitesimal change in x, representing integration with respect to x.In this article will explain what "dx" represents in integration and ...
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Application of Integrals
Last Updated: 24 February 2026
Integrals are used to find the area and volume of various 2-D and 3-D curves, and they have vast applications in the fields of mathematics and physics. They generally help...
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How to Calculate a Definite Integral?
Last Updated: 23 July 2025
A definite integral is a mathematical concept used in calculus to calculate the total effect of a function over a given time frame. It represents the net area between the ...
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Integration Formulas
Last Updated: 23 July 2025
Integration Formulas are the basic formulas used to solve various integral problems. They are used to find the integration of algebraic expressions, trigonometric ratios, ...
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How to solve Differential Equations?
Last Updated: 08 November 2025
A differential equation is an equation that involves an unknown function and its derivatives. Mathematically, equations that contain an independent variable, a dependent ...
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Chain Rule: Theorem, Formula and Solved Examples
Last Updated: 01 November 2025
The Chain Rule is a way to find the derivative of composite functions. It is one of the basic rules used in mathematics for solving differential equations. It helps us to ...
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Application of Derivatives
Last Updated: 10 February 2026
Derivative of a variable y with respect to x is defined as the ratio between the change in y and the change in x, depending upon the condition that changes in x should be ...
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Integration of Trigonometric Functions
Last Updated: 02 December 2025
Integration is the process of summing up small values of a function in the region of limits. It is just the opposite of differentiation. Integration is also known as an an...
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Integration by Substitution Method
Last Updated: 02 December 2025
Integration by substitution method can be used whenever the given function f(x) and its derivative f'(x) are multiplied and given as a single function, i.e. the given func...
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Implicit Differentiation
Last Updated: 23 July 2025
Implicit Differentiation is the process of differentiation in which we differentiate the implicit function without converting it into an explicit function. For example, we...
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Logarithmic Differentiation
Last Updated: 23 July 2025
Method of finding a function's derivative by first taking the logarithm and then differentiating is called logarithmic differentiation. This method is specially used when ...
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Power Rule
Last Updated: 16 April 2026
The power rule is a basic rule in calculus used to find the derivative of expressions like xn.Rule: Since differentiation is a linear operation on the space of differentia...
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Product Rule in Derivatives
Last Updated: 01 November 2025
The product rule in calculus is the fundamental rule and is used to find the derivative of functions. The Product Rule of calculus is proved using the concept of limits an...
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