How To Get Answers and Steps For a Function of a Function Differentiation (Calculus) Problem Using The Calculator Encyclopedia

Last Updated on February 12, 2024

cIn this guide, we unveil the step-by-step process of solving function of a function differentiation (calculus) problems using the calculator encyclopedia. Whether you’re tackling basic derivatives or diving into complex calculus concepts, our article provides clear explanations and practical examples to help you understand and conquer these problems effortlessly.

According to Wikipedia, in mathematics, differential calculus is a sub-field of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus, the study of the area beneath a curve.

Nickzom Calculator for Differentiation in Calculus

Nickzom Calculator calculates function of a function differentiation (calculus) for the following formats:

• (expression)ⁿ
• k(expression)ⁿ
• sin(expression)
• ksin(expression)
• cos(expression)
• kcos(expression)
• tan(expression)
• ktan(expression)
• sinh(expression)
• ksinh(expression)
• cosh(expression)
• kcosh(expression)
• cot(expression)
• kcot(expression)
• cosec(expression)
• kcosec(expression)
• In(expression)
• kIn(expression)
• log_a(expression)
• klog_a(expression)
• e^(expression)
• ke^(expression)
• a^(expression)
• ka^(expression)

k, a and n in the formats above represents constants.

The expression represents a polynomial, quadratic or linear mathematical statement, such as:

• 3x + 5
• 4x² + 2x + 1
• 2x³ + 7x + 12
• 5x⁴ + 3x³ + 4x² + 12x + 15

So implementing the expressions and applying constant numbers here is a list of what the function of a function formats look like that can be solved by Nickzom Calculator and also display the steps (workings).

• • (2x² + 3x + 5)⁷
  • 4(2x + 1)⁶
  • sin(2x² + 3x + 5)
  • 2sin(3x + 5)
  • cos(3x + 5)
  • 2cos(3x + 5)
  • tan(2x³ + 3x² + 4x + 5)
  • 3tan(7x + 6)
  • sinh(2x⁴ + 12)
  • 2sinh(3x + 10)
  • cosh(x⁵ + 2x³ + 11)
  • 3cosh(2x³ + 12x + 17)
  • cot(2x + 1)
  • 3cot(3x + 5)
  • cosec(x + 12)
  • 7cosec(2x + 7)
  • In(x³ + 2x + 7)
  • 2In(2x² + 3x + 12)
  • log₃(3x + 7)
  • 2log₂(x² + 4x + 8)
  • e^{(3x + 5)}
  • 2e^{(2x + 3)}
  • 2^{(7x + 2)}
  • 7 . 2^{(6x + 7)}

Function of a Function makes use of the chain rule

^dy/_dx = ^dy/_du x ^du/_dx

Using the calculator encyclopedia – Nickzom Calculator for your calculus problem makes work very easy and faster for you on all fronts.

How to Access Nickzom Calculator

You can access Nickzom Calculator (The Calculator Encyclopedia) via any of these channels:

Web – https://www.nickzom.org/calculator-plus

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

To begin getting answers for a function of a function calculus differentiation problem, it is best to obtain the Nickzom Calculator professional version (Nickzom Calculator+). You have three choices to reach to the page or activity for performing the Function of a Function operation.

First Choice:

Proceed to the Calculator Map, click on Calculus under the Engineering Section

On the Calculus, Page or Activity, click on Differentiation

On the Differentiation Page or Activity, click on Function of a Function

After clicking on the Function of a Function, you get directed to the page or activity for you to input your values and get your answer and workings. The screenshot of the page is shown below. I would love to show you the two other ways you can reach this page from the app.

Second Choice:

Select Engineering and click on Open Section in the Home Page

Then, click on Calculus in the Engineering section

This now takes us to the Calculus page, now click on differentiation and then on function of a function on the differentiation page.

Third Choice:

This choice is the fastest way to the function of a function activity

At the home page, type function of a function in the search box

Click on Search or press Enter, then a search result gets displayed. Click on Calculate Differentiation | Function

Search Result on Web

Search Result on App

On clicking on Calculate Differentiation | Function, you get directed to the Function of a Function page.

For the purpose of this post let us get answers to two function of a function calculus problems which are:

• sin(3x + 5)
• (2x² + 3x + 5)³

First Example:

We need to identify the function format for Nickzom Calculator to solve for sin(3x + 5) and this format is sin(expression). Therefore, we select sin(expression)

Then, Click on Calculate, you are now required to enter the degree of your expression. Our expression is 3x + 5, therefore, the degree is 1.

You can simply check out this link to Math is Fun to see how to know the degree of a mathematical expression in case you do not know.

Enter 1 as the degree of the expression and click on Calculate. An input format is displayed for you to enter the appropriate values.

Since our function of a function problem is sin(3x + 5). What’s next is for us to fill in the appropriate data or values; 3 as the coefficient of x and 5 as the constant like in the screenshot below.

Lastly, click on Calculate, Nickzom Calculator would work its magic by solving this problem and displaying the answer alongside the formula and workings for you as seen in the screenshots below.

Second Example:

Just like we did in the first example, we need to identify the function format that fits this calculus problem of (2x² + 3x + 5)³ and the format is (expression)ⁿ. Now we select the format (expression)^n and click on calculate.

We need to enter the degree of our expression and since the expression is 2x² + 3x + 5, the degree is 2.

Again, you can simple check out this link to Math is Fun to see how to know the degree of a mathematical expression in case you do not know.

Now, enter 2 as the degree of the expression and click on Calculate

Nickzom Calculator now provides an input form for you to properly enter the values according to the right coefficients.

Then, click on Calculate for Nickzom Calculator to do its magic.

Now, that’s it. You can see a lot of the wonders of Nickzom Calculator by trying the various formats for a Function of a Function in differential calculus.