Introduction to Product Rule Calculator:
Product rule calculator with steps is the best online source that is used to evaluate the derivation of product rule. It helps to find the differentiation of the product rule of two or more than two functions.
Product rule derivative calculator is a useful tool for students, teacher, professional or researcher who wants to find the product rule derivation function solution.
What is the Product Rule?
Product rule is the process in calculus, used to find the derivation of product of two or more than two functions. For example, the first function is f(x) and the second function is g(x). The product rule of f(x) . g(x) formula used by the derivative calculator product rule is,
$$ (f(x) . g(x))’ \;=\; f’(x) . g(x) + f(x) . g’(x) $$
The product rule function is f(x) . g(x) and its differentiation is (f(x) . g(x))`. This rule is essential in different fields such as mathematics, economics, physics and engineering etc.
How to Find Derivative Product Rule?
The product rule is a systematic method to find the derivative function that cannot be solved with direct differential rule. Here’s a step-by-step guide on how to apply the product rule:
Step 1:
Identify the two functions that is being multiplied. Suppose you have a product of functions f(x) and g(x).
$$ h(x) \;=\; f(x) ⋅ g(x) $$
Step 2:
Differentiate each function f(x) and g(x) with respect to x separately. Find f′(x), the derivative of f(x) and g′(x), the derivative of g(x).
Step 3:
Use the product rule formula and add the value of f`(x) and g`(x),
$$ (f(x) . g(x))’ \;=\; f’(x) . g(x) + f(x) . g’(x) $$
Step 4:
Simplify the expression after adding the value of f(x) and g(x) and its derivation value respectively.
Step 5:
After simplification, you get the solution of your given product rule derivation function.
By following these steps, you can easily apply the product rule to find the derivative of the product of functions.
Practical Example of Product Rule:
The example of product rule derivation problem will help you in the conceptual clarity of calculation process of product rule calculator with steps.
Example: Differentiate the following:
$$ y \;=\; x^{-2} (4 + 3x^{-3}) $$
Solution:
Differentiate with respect to x,
$$ y’ \;=\; x^{-2} D[4 + 3x^{-3}] + D[x^{-2}] (4 + 3x^{-3}) $$
$$ =\; x^{-2} (-9x^{-4}) + (-2x^{-3})(4 + 3x^{-3}) $$
$$ =\; -9x^{-6} - 8x^{-3} - 6x^{-6} $$
$$ =\; -15x^{-6} - 8x^{-3} $$
$$ =\; \frac{-15}{x^6} - \frac{8}{x^3} $$
$$ =\; \frac{-15}{x^6} - \frac{8x^3}{x^6} $$
$$ =\; -\frac{15 + 8x^3}{x^6} $$
How to Use the Product Rule Calculator?
The derivative calculator product rule has an easy-to-use interface, so you can easily evaluate the derivative of a product function. Before adding the input, you must follow some simple steps that are:
- Add the product rule problems that you want to differentiate in the input box.
- Choose the variable of product rule derivation from its respective field.
- Recheck your input value for product rule derivation before hitting the calculate button of product rule derivative calculator.
- The “Calculate” button gives the desired result of your given product rule problem.
- If you want to try our product rule solver for checking its accuracy in solution then use the load example option.
- The “Recalculate” button brings you to a new page for solving more product rule derivation questions.
Outcome from Product Rule Derivative Calculator:
The derivative calculator product rule with steps gives you the solution of differential problem when you give the input. It gives you the result as:
- Result Option:
When you click on the result option, it provides you the solution of product rule derivation questions.
- Possible Steps:
When you click on the possible steps option then the product rule calculator with steps provides you the step by step solution of product rule of differential problem.
Benefits of Derivative Calculator Product Rule:
The product rule calculus calculator gives you multiple benefits whenever you use it to calculate product rule of given function. These benefits are:
- The product rule derivative calculator saves the time and effort that you consume in solving complex product rule questions.
- It is a free-of-cost tool that provides you the solution of given product rule problem for free.
- The product rule solver is an adaptive tool that helps you to evaluate inverse trigonometry, logarithmic, exponential, algebraic functions.
- It can assist you in practicing different product rule functions problems which help you to get grip on this concept.
- It gives you accurate solution of product rule differential problems without any difficulty.
- Product rule calculator with steps can operated on online platform which means you can use it anytime.
