A power function is when we have any variable x to the power of any real number represented here as n.
In the formula sheet we are given the equation:
So basically all we do is multiply our function by the power term and then minus one the power term by one.
Say we have x to the power of negative fraction:
We still follow the same procedure of multiplying the function by the power term and then minus it by one.
A polynomial is basically a combination of power functions. So while they may appear to be more tricky, if we isolate each term, they are just as easy as the example above.
Given the equation below find the derivative:
you first need to rewrite it so that it looks more straightforward:
Then just follow the simple rule: bring the power down, put it in front, and take one away from the power.
Lets start with first term:
The second term:
The plus 4 at the end of equation is eliminated, as it has no x component.
To find we simply add these terms together
The exponential functions that we focus on in maths methods is
This is Euler’s number to the power of a variable x and has a remarkable differentiation property
In the formula sheet we are provided with the very useful formula:
This is one of the easiest rules to follow as all you do is multiply the exponential component by the coefficient of x
Let’s try to find the derivative for this function
If we follow the formula provided, it greatly simplifies the process
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