# What is the difference between the chain rule and the power rule? Are they simply different forms of each other?

They are very different !

The "power rule" is used to differentiate a fixed power of

The "chain rule" is used to differentiate a function of a function, e.g.

Chain Rule

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The chain rule and the power rule are two distinct concepts in calculus. The power rule is used to find the derivative of a function that is raised to a constant power, whereas the chain rule is used to find the derivative of composite functions. They are not simply different forms of each other. The power rule states that if you have a function ( f(x) = x^n ), its derivative is ( f'(x) = nx^{n-1} ), where ( n ) is a constant. The chain rule, on the other hand, deals with finding the derivative of a function composed of two or more functions. It states that if you have a composite function ( f(g(x)) ), the derivative of ( f(g(x)) ) with respect to ( x ) is ( f'(g(x)) \cdot g'(x) ), where ( f'(g(x)) ) represents the derivative of ( f ) with respect to ( g(x) ), and ( g'(x) ) represents the derivative of ( g ) with respect to ( x ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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