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What is Differentiation?
Differentiation is the process of identifying and then catering to the specific needs of students in the classroom. This can be done in a variety of ways, such as by providing different instruction or assignments for students of different abilities, or by grouping students together based on their needs. Differentiation helps ensure that all students have the opportunity to learn and achieve their fullest potential. Chain Rule – Statement and Steps to be Followed.
The Chain Rule Derivative States that:
The derivative of the function ƒ(x) at the point x is equal to the derivative of ƒ at x multiplied by the derivative of x at the point x.
The Chain Rule Derivative can be used to calculate the derivative of a composite function ƒ(g(x)), where ƒ is the outer function and g is the inner function. To calculate the derivative using the Chain Rule Derivative, first calculate the derivative of ƒ at x, and then multiply that result by the derivative of g at x.
Chain Rule Differentiation:
The chain rule for differentiation states that the derivative of a composite function can be found by taking the derivative of the inner function with respect to x and then multiplying by the derivative of the outer function with respect to x.
Let’s look at an example:
The function y = f(x) = x2 is composed of two functions, x2 and f(x). The derivative of y with respect to x can be found by taking the derivative of x2 with respect to x, and then multiplying by the derivative of f(x) with respect to x.
dy/dx = 2x
then, dy/dx = (2x) * (df/dx)
then, dy/dx = 2
Steps to be Followed While Using Chain Rule Formula –
Step 1:
First, identify the function that is being differentiated. In this example, it is the function y = f(x).
Step 2:
Next, identify the power of the x-variable in the function. In this example, it is x3.
Step 3:
Now, use the chain rule to differentiate the function. In this example, the differentiated function would be y’ = 3x2f(x).
Chain Rule – Statement and Steps to be Followed.
