physics604 said:Homework Statement
Find the derivative of y=cos(a3+x3)
Homework Equations
Chain rule
The Attempt at a Solution
y=cosu
[itex]\frac{dy}{du}[/itex] = -sinu
u=a3+x3
[itex]\frac{du}{dx}[/itex] = 3a2+3x2
physics604 said:I don't know how to make the equations like yours.
The chain rule is a formula in calculus used to find the derivative of composite functions. It states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.
The chain rule is applied in derivatives by first identifying the outer function and the inner function. Then, the derivative of the outer function is evaluated at the inner function, and finally, the derivative of the inner function is multiplied by this result to get the overall derivative of the composite function.
Yes, the chain rule can be used for any type of composite function, as long as the functions are differentiable. This means that the functions must have a defined derivative at every point in their domain.
No, there are other methods such as the product rule and quotient rule, but the chain rule is the most commonly used method for finding derivatives of composite functions.
The chain rule should be used when the function you are trying to find the derivative of is a composition of two or more functions. It is also helpful to use the chain rule when the functions involved are more complicated and cannot be easily differentiated using other rules.