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The derivative of a function describes the function's instantaneous rate of change at a certain point. Another common interpretation is that the derivative gives us the slope of the line tangent to the function's graph at that point. Learn how we define the derivative using limits. Learn about a bunch of very useful rules (like the power, product, and quotient rules) that help us find ...
- Secant Lines
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- Product Rule
Discover the product rule, a fundamental technique for...
- Differentiate Products
Find the derivatives of products of basic functions.
- Secant Lines
- What Is Differentiation in Maths
- Differentiation Formulas
- Differentiation Rules
- Real-Life Applications of Differentiation
- Solved Examples
- Video Lesson on Class 12 Important Calculus Questions
In Mathematics, Differentiation can be defined as a derivative of a function with respect to an independent variable. Differentiation, in calculus, can be applied to measure the function per unit change in the independent variable. Let y = f(x) be a function of x. Then, the rate of change of “y” per unit change in “x” is given by: dy / dx If the fu...
The important Differentiation formulasare given below in the table. Here, let us consider f(x) as a function and f'(x) is the derivative of the function. Also, see:
The basic differentiation rules that need to be followed are as follows: 1. Sum and Difference Rule 2. Product Rule 3. Quotient Rule 4. Chain Rule Let us discuss all these rules here.
With the help of differentiation, we are able to find the rate of change of one quantity with respect to another. Some of the examples are: 1. Acceleration: Rate of change of velocity with respect to time 2. To calculate the highest and lowest point of the curve in a graph or to know its turning point, the derivative function is used 3. To find tan...
Q.1: Differentiate f(x) = 6x3 – 9x + 4 with respect to x. Solution: Given: f(x) = 6x3 – 9x + 4 On differentiating both the sides w.r.t x, we get; f'(x) = (3)(6)x2– 9 f'(x) = 18x2– 9 This is the final answer. Q.2: Differentiate y = x(3x2– 9) Solution: Given, y = x(3x2– 9) y = 3x3– 9x On differentiating both the sides we get, dy/dx = 9x2– 9 This is t...
Practice Problems
1. Find the derivative of the function f(x) = 3 sin x + cos x – tan x. 2. Perform the differentiation for the following functions: (i) f(x) = x3 sin 2x (ii) g(x) = 4xe2x− 9x 3. Find the derivative of the function f(x) = x/(x – 2) (i) Using the limit definition of differentiation (ii) Using the quotient rule To know more about Differentiation and any Maths related topics, please visit us at BYJU’S.
It means that, for the function x 2, the slope or "rate of change" at any point is 2x. So when x=2 the slope is 2x = 4, as shown here: Or when x=5 the slope is 2x = 10, and so on. Note: f’ (x) can also be used to mean "the derivative of": f’ (x) = 2x. "The derivative of f (x) equals 2x". or simply "f-dash of x equals 2x".
Aug 17, 2024 · Tangent Lines. We begin our study of calculus by revisiting the notion of secant lines and tangent lines. Recall that we used the slope of a secant line to a function at a point \((a,f(a))\) to estimate the rate of change, or the rate at which one variable changes in relation to another variable.
v. t. e. In mathematics, the derivative is a fundamental tool that quantifies the sensitivity of change of a function 's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
Its definition involves limits. ... For this example, the derivative is: ... we'll practice differentiating functions using the definition of the derivative.
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Derivative. The derivative of a function is the rate of change of the function's output relative to its input value. Given y = f (x), the derivative of f (x), denoted f' (x) (or df (x)/dx), is defined by the following limit: The definition of the derivative is derived from the formula for the slope of a line. Recall that the slope of a line is ...
