arunbg said:Chain rule goes something like
dy/dx=dy/du*du/dv*...*df/dx .
It is usually used when you when you have a nested combination of functions, ie functions within functions.
For your question, you need to use both the quotient rule as well as the chain rule ( (1+x^2)^2, which is the funtion 1+x^2 within a squaring function ) .
Can you finish your problem now ?
l46kok said:Right.. that's the BRUTE force way to do it.
I was wondering if there was a way to finish this without even applying the quotient rule
suspenc3 said:if you don't want to use the quotient rule you can bring the denominator up top so:[tex] y= 2x (1+x^2)^{-2}[/tex] now use the product rule
The chain rule is a formula used in calculus to find the derivative of a composite function. It allows us to take the derivative of an outer function and multiply it by the derivative of the inner function.
The chain rule is important because it allows us to find the derivative of more complex functions by breaking them down into smaller, more manageable parts. It is a fundamental concept in calculus and is used in many real-world applications.
To apply the chain rule, you must first identify the inner and outer functions of the composite function. Then, take the derivative of the outer function and multiply it by the derivative of the inner function, which is found by substituting the inner function into the derivative of the outer function.
Sure, let's say we have the function f(x) = (2x^2 + 3)^5. The inner function would be 2x^2 + 3 and the outer function would be x^5. To find the derivative, we would first take the derivative of the outer function, which is 5x^4. Then, we substitute the inner function into this derivative, giving us 5(2x^2 + 3)^4 * 4x = 20x(2x^2 + 3)^4. This is the derivative of the original function f(x).
Some common mistakes when using the chain rule include forgetting to take the derivative of the outer function, not substituting the inner function into the derivative correctly, and not applying the chain rule to all parts of the function. It is important to double check your work and practice using the chain rule to avoid these mistakes.