The chain rule formula states that F'(𝑥) = f'(g(𝑥).g'(𝑥), where g(𝑥) is the inner function and f(𝑥) is the outer function. We will now use the chain rule formula to differentiate this function. So we must multiply the result of 5(4𝑥 – 3) 4 by 4. The inner function is the function inside the brackets. we already have 5(4𝑥 – 3) 4 and now we must multiply this by the derivative of the inner function. Multiply this by the derivative of the inner functionįrom step 1.
However because we have 4𝑥 – 3 inside the brackets and not just 𝑥, we must also include step 2. We keep the inner function of 4𝑥-3 the same, so we write 5(4𝑥 – 3) 4. 𝑥 5 would differentiate to 5𝑥 4 and so we write ( ) 5 differentiated as 5( ) 4. We differentiate this like we would 𝑥 5. Differentiate the outer function, keeping the inner function the same We define 4𝑥 – 3 as the inner function and the ( ) 5 as the outer function. Below this, we will use the chain rule formula method. In this example we will use the chain rule step-by-step. Multiply this by the derivative of the inner function.įor example, differentiate (4𝑥 – 3) 5 using the chain rule.Differentiate the outer function, keeping the inner function the same.
#Calculus chain rule problems how to#
How to Do the Chain Rule To do the chain rule:
The function must be a composite function of two or more functions.To use the chain rule, the following rules are required: In words, the chain rule requires finding the derivative of the outer function while keeping the inner function the same and then multiplying this by the derivative of the inner function. g(𝑥) is the inner function and f(𝑥) is the outer function. The chain rule is defined as, where u is a function of 𝑥 ( u = g(x) ) and y is a function of u ( y = f(u) ).Īlternatively, the chain rule can be written in function notation as F'(𝑥) = f'(g(𝑥)).g'(𝑥), where F(𝑥) = f(g(𝑥)). The chain rule is used when a function is within another function.
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