A derivative calculator typically takes the input function and uses mathematical formulas and algorithms to compute the derivative of the function. There are several techniques for computing derivatives, such as the power rule, product rule, chain rule, and quotient rule, among others.
What is Derivative Calculator
Some derivative calculators are simple and only accept basic input functions, while others are more complex and can handle more advanced functions. Many derivative calculators are available online and can be accessed for free. Some are standalone applications, while others are integrated into more comprehensive math software packages.
The use of a derivative calculator can save time and effort in solving problems involving derivatives, especially for those who are not comfortable with the underlying mathematical concepts or who need to solve complex problems quickly. However, it is important to understand the basic principles of calculus and how to derive functions by hand, as this knowledge is essential for a deeper understanding of the subject and for more advanced applications.
Formula of Derivative Calculator and Example
The formula used by a derivative calculator to calculate the derivative of a function depends on the type of function being evaluated.
For example, the derivative of a polynomial function can be found using the power rule, which states that the derivative of a term with a variable raised to a power is equal to the product of the exponent and the coefficient of the term, multiplied by the variable with the exponent decreased by 1.
The derivative of a trigonometric function can be found using trigonometric identities and rules such as the chain rule and product rule.
In general, the formula for the derivative of a function can be written as:
f'(x) = lim h->0 [f(x+h) – f(x)] / h
where f'(x) represents the derivative of the function f(x) at the point x, and h is a small value representing the change in the input variable.
A derivative calculator will use various algorithms and rules to calculate the derivative of a given function based on its type and complexity.
As an example, consider the function f(x) = x^3 – 2x^2 + 4x – 3. To find its derivative using the power rule, we differentiate each term of the function with respect to x, as follows:
f'(x) = 3x^2 – 4x + 4
Thus, the derivative of the function f(x) is f'(x) = 3x^2 – 4x + 4.
Using a derivative calculator, we can quickly verify this result by inputting the function f(x) and selecting the option to calculate its derivative. The calculator will then output the derivative of the function as 3x^2 – 4x + 4, which matches our result obtained using the power rule.