If you’ve gotten your brains smashed like fruits due to calculus formulas, it is time to get its juice. We mean that in a better way for sure! But, jokes apart, here you are going to learn some really important calculus formulas that will make your calculus voyage buttery smooth.
Can you work with derivative formula?
The concept of derivate forms a crucial part of calculus and so does the derivative formula. You can find the derivative of a function by using the derivative formula mentioned below:
Derivative D = (d/dx) (F), where D is the derivative and F is the given function. This is basically the first order derivative.
Example: Find the derivative of the function F = 5x.
Solution: Here, F = 5x; so D = (d/dx) (5x) => D = 5.
Note: Derivative of a constant is always zero.
Can you use the average rate of change formula?
The average rate of change formula is given by A(x) = f (b) – f (a) / b – a, where a and b are the numeric values and f (a) and f (a) are the function values that are found out by putting a and b in the function f(x).
Example: Apply the average rate of change formula on the function f(x) = 2x + 1 from the values 2 to 1.
Solution: firstly, let us calculate f(1) = 2(1) + 1 => f(1) = 3.
Now, f (2) = 2(2) + 1 => f (2) = 5. Therefore, substituting the values of f (1) and f (2) in the average rate of change formula, we get A = 5 – 3 / 2 – 1 => A = 2 / 1 => A = 2.
The solved examples above demonstrate the application of both the derivative formula and the average rate of change formula in a detailed way.