Expert reviewed • 05 March 2025 • 8 minute read
Note:
Video coming soon!
Note:
Video coming soon!
Building on our knowledge of differentiation from the year 11 course, we should know that there are three standard derivative formulas for exponential functions:
It should be noted that the base formula for deriving is also . However, when deriving the expression , it is important to note that the negative sign is moved out the front, as follows: .
Derive the following function using the product rule, and any related formulas provided above.
First we must determine the values of and .
Using differentiation formulas and techniques learnt so far, find and :
Finally, we can substitute these values into the product rule formula, to determine the derivative:
Note:
Video coming soon!
To begin our understanding of differentiating logarithmic functions, it is important to start with the reciprocal function. This is a function of base denoted by the formula:
Differentiate the function,
Applying the formula above we can simply differentiate:
Now that we have learnt the general formula for the reciprocal function, there are two other standard formulas, which are important for us to apply to various questions.
By manipulating any expression or equation to fit the form of the formulas above, functions with base can be easily solved.
Differentiate the function using both the quotient rule, and any related formulas provided above.
We must first determine terms and to use in the quotient rule:
Using differentiation formulas and techniques learnt so far, find and :
Finally, we can substitute these values into the quotient rule formula, to determine the derivative: