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Differential Calculus 6 units · 117 skills. Unit 1 Limits and continuity. Unit 2 Derivatives: definition and basic rules. Unit 3 Derivatives: chain rule and other advanced topics. Unit 4 Applications of derivatives. Unit 5 Analyzing functions. Unit 6 Parametric equations, polar coordinates, and vector-valued functions. Course challenge.
- Secant Lines
AP®︎/College Calculus AB; AP®︎/College Calculus BC;...
- Product Rule
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- Differentiate Products
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- 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.
f’ (x) = lim Δx→0 f (x+Δx) − f (x) Δx. "The derivative of f equals. the limit as Δ x goes to zero of f (x+Δx) - f (x) over Δx ". Or sometimes the derivative is written like this (explained on Derivatives as dy/dx): dy dx = f (x+dx) − f (x) dx. The process of finding a derivative is called "differentiation".
Jul 31, 2024 · Differentiation of Trigonometric Functions is the derivative of Trigonometric Functions such as sin, cos, tan, cot, sec, and cosec. Differentiation is an important part of the calculus. It is defined as the rate of change of one quantity with respect to some other quantity. The differentiation of the trigonometric functions is used in real life in
Differentiation. The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity. The laws of Differential Calculus were laid by Sir Isaac Newton. The principles of limits and derivatives are used in many disciplines of science.
3.3.6 Combine the differentiation rules to find the derivative of a polynomial or rational function. Finding derivatives of functions by using the definition of the derivative can be a lengthy and, for certain functions, a rather challenging process.
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3.3: Differentiation Rules. The derivative of a constant function is zero. The derivative of a power function is a function in which the power on x becomes the coefficient of the term and the power on x in the derivative decreases by 1. The derivative of a constant c multiplied by a function f is the same as the constant multiplied by the ...
