It looks like you completely missed the fact that this is a quotient (use the quotient rule first). As part of using the quotient rule, you'll need the chain rule.Mathysics said:Homework Statement
f(x) = ((x^2+2)^2)/(x+2)^1/2
Use the chain rule to find the derivative
Homework Equations
None
The Attempt at a Solution
((x^2+2)^2)(x+2)^-1/2
PS: Answer in the book is 3x((x^2+2)^1/2)
I have no idea how they get it there, would like some help, thx!
Mark44 said:It looks like you completely missed the fact that this is a quotient (use the quotient rule first). As part of using the quotient rule, you'll need the chain rule.
The chain rule is a mathematical rule used to find the derivative of a composite function, which is a function that is made up of two or more functions. 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 should be used when you have a composite function and need to find its derivative. This usually occurs when you have a function within a function, such as f(g(x)).
To apply the chain rule, you first need to identify the outer function and the inner function. Then, you can use the formula: (d/dx)f(g(x)) = f'(g(x)) * g'(x), where f'(g(x)) represents the derivative of the outer function and g'(x) represents the derivative of the inner function.
Sure, let's say we have the function f(x) = sin(3x). To find its derivative, we can first identify the outer function, which is sin(x). Then, we can identify the inner function, which is 3x. Applying the chain rule, we get f'(x) = cos(3x) * 3 = 3cos(3x).
One common mistake is forgetting to take the derivative of the outer function. Another mistake is mixing up the order of operations and finding the derivative of the outer function before multiplying by the derivative of the inner function. It's important to carefully identify and follow the steps of the chain rule to avoid these mistakes.