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.