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These are some examples of common derivatives that require the chain rule.
The chain rule applies when a differentiable function is applied to another differentiable function. The power rule applies when a differentiable function is raised to a power. Quotient rule applies when differentiable functions are divided. The product rule applies when differentiable functions are multiplied. If there exists a derivative for f(x) and g(x), and c and n are real numbers the following are true: The function must be differentiable over the interval (a,b) and a < c < b. This is a method to approximate the derivative. Using limits the derivative is defined as: The derivative is way to define how an expressions output changes as the inputs change. Limit Evaluation Methods Continuous Functionsĭerivatives Math Help Definition of a Derivative The following expression states that as x approaches infinity, the value c is a very large and positive number, the function approaches the value L.Īlso the limit as x approaches negative infinity, the value of c is a very large and negative number, is expressed below. The following expression states that as x approaches the value c and x < c the function approaches the value L. The following expression states that as x approaches the value c and x > c the function approaches the value L. The following expression states that as x approaches the value c the function approaches the value L. This value can be any point on the number line and often limits are evaluated as an argument approaches infinity or minus infinity. The limit is a method of evaluating an expression as an argument approaches a value.
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