Expert reviewed • 05 March 2025 • 6 minute read
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So far in this module, we have not discussed how to use calculus, when a logarithmic function has a base other than . Before we can use any type of formula to derive a function in the form , we must first learn how to change it's base. The formula for this is as follows:
Although the change of base formula is useful in deriving a function, a simpler method is to utilise the following formula.
Differentiate the following function:
Applying the formula above, we can determine the derivative of this function:
Additionally in this module, we have not explored using calculus with exponential functions that have bases other than . Before we can use any formula to derive a function in the form , we must first revise how to change its base.
Now that we know how to change the base of a function in the form , we can apply calculus to these functions in two different ways.
Differentiate the following function:
Using the formulas provided above, we can derive this function by substituting terms into the formula.
In this case the negative sign is not attached to the value of 2, and thus is treated as a multiplication factor of the derivative.
Solve the following expression:
Using the formulas provided above and previously learned knowledge, we can evaluate the given definite integral.