The chain rule is the rule which is used in finding the derivatives of composite functions. The chain rule state that (in respect to an equation) the instant rate of change of the ‘f’ relative in respect of ‘g’ relative helps us to calculate the rate of change of ‘f’ relative in respective of ‘x’ relative. Let us learn more about the chain rule.
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Definition of the Chain Rule
The chain rule is such a rule which is also known as the outside-inside rule or the composite function rule or this is also known as the function of a function rule. The Chain rule is only used while finding the derivatives of the composite functions.
Spell the Theorem of Chain Rule
In order to understand the theorem of the chain rule, let us consider ‘f’ to be a real-valued function. This f is the composite value of two functions g and h. Now we will consider u = h(x), whereas du/dx and dg/dy will exist and thereby it will be expressed as Change in f/ Change in x = Change in g/ Change in u X change in u/ change in x. This is simplified in the form of an equation which is – df/dx = dg/du .du/dx. Visit Here
What are the Steps Involved in Chain Rule?
The steps which are involved in the process of Chain Rule are as follows:
- Step 1: Firstly, you need to identify the chain rule. You can identify a chain rule by checking if the function is a composite function, this will mean that one function is being nested over the other function.
- Step 2: Now you need to identify the inner and the outer function.
- Step 3: Next, find the derivative of the outer function.
- Step 4: Now find the derivative of the inner function.
- Step 5: Multiply steps 3 and 4
- Step 6: Now you can simplify the chain rule derivative.
What Do You Mean by Product Rule?
The product rule in the study of calculus is a method to find out the derivative or the differentiation of the function which is given in the form of two different functions. This means, here we can apply the product rule or the chain rule. This will be done to derive the function in the form which is given as f(x)·g(x). This product rule will follow the study of limits and the derivatives which is done in the derivation.
Product Rule in Calculus
In calculus as well, the product rule proves to be useful. The product rule is useful in finding the derivative of any function which is given in the form of a product, which is obtained by the process of multiplication of either of the differentiable functions.
The product rule states that – The derivative of the product having two differentiable functions will be equal to the sum of the product having the second function with differentiation of the first function and the product of the first function with the differentiation done with the second function.
What is the Product Rule Formula?
The estimation of the derivative or evaluation of the differentiation of the product of the two functions can be done with the help of two formulae in the study of Calculus. The formula is given as follows:
ddxddx f(x) = ddxddx {u(x)·v(x)} = [v(x) × u'(x) + u(x) × v'(x)]
In this case,
- f(x) = This is termed as the product of the functions that are differentiable taht is u(x) and v(x).
- u(x), v(x) = These are termed as the Differentiable functions
- u'(x) = This is the Derivative of function u(x)
- v'(x) = While, this is the Derivative of the function v(x)
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