Derivatives of Combinations of Functions
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Sum or Difference of Functions:
If and are differentiable, then:
This means if you want to find the rate of change of two functions added or subtracted, you can find the derivative of each and then add or subtract them.
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Scalar Multiplication:
If is a constant and is differentiable:
This means if you multiply a function by a number, you can find the derivative by multiplying that number by the derivative of the function.
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Product Rule:
If and are differentiable, then:
This is called the product rule, which is used when two functions are multiplied together.
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Quotient Rule:
If and are differentiable, then the derivative of the quotient is:
This is called the quotient rule, used when one function is divided by another.