![]() The chain rule formula states that F'(□) = f'(g(□).g'(□), where g(□) is the inner function and f(□) is the outer function. We will now use the chain rule formula to differentiate this function. So we must multiply the result of 5(4□ – 3) 4 by 4. The inner function is the function inside the brackets. we already have 5(4□ – 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 4□ – 3 inside the brackets and not just □, we must also include step 2. We keep the inner function of 4□-3 the same, so we write 5(4□ – 3) 4. ![]() □ 5 would differentiate to 5□ 4 and so we write ( ) 5 differentiated as 5( ) 4. We differentiate this like we would □ 5. Differentiate the outer function, keeping the inner function the same We define 4□ – 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 (4□ – 3) 5 using the chain rule.Differentiate the outer function, keeping the inner function the same.How to Do the Chain Rule To do the chain rule: Such functions must be differentiable themselves.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(□) is the inner function and f(□) is the outer function. The chain rule is defined as, where u is a function of □ ( 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'(□) = f'(g(□)).g'(□), where F(□) = f(g(□)). The chain rule is used when a function is within another function.
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