You did use the chain rule , along with the product rule.hadizainud said:Homework Statement
Differentiate the functions using chain rule. 2(x3 −1)(3x2 +1)4
Homework Equations
Chain Rule = f ' (g(x))g' (x)
The Attempt at a Solution
I don't know how to do using chain rule, but product rule is easier
So using product rule,
= f ' (x) g(x) + f (x)g' (x)
= (2)(x3-1)0(3x[SUPdid]2[/SUP])(3x2+1)4 + 2(x3-1)(4)(3x2+1)3(6x)
= (2)(3x2)(3x2+1)4 + 8(x3-1)(3x2+1)3(6x)
Can anyone show me how to do it, using chain rule?
hadizainud said:I need your help on my previous topic.
Please do help me :)
https://www.physicsforums.com/showthread.php?t=559855
The chain rule is a mathematical rule that allows you to find the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function.
The chain rule is important because it allows us to find the derivative of more complex functions that are made up of multiple functions. It is a fundamental tool in the study of calculus and is used to solve a wide range of problems in fields such as physics, engineering, and economics.
To apply the chain rule, you first identify the inner and outer functions in the composite function. Then, you find the derivative of the outer function and the derivative of the inner function. Finally, you multiply these two derivatives together to find the derivative of the composite function.
Sure, let's say we have the function f(x) = (x^2 + 3x)^3. The inner function is x^2 + 3x and the outer function is x^3. Using the chain rule, we can find the derivative of f(x) as follows: f'(x) = 3(x^2 + 3x)^2 * (2x + 3) = 3(2x^2 + 6x)(2x + 3) = 6x^2 + 18x + 9.
Yes, some common mistakes when using the chain rule include forgetting to find the derivative of the outer function, mixing up the order of the derivatives, and not properly applying the product rule when multiplying the derivatives together. It is important to be careful and double check your work when using the chain rule to avoid these errors.