Derivative Calculator

This Derivative Calculator helps you find the derivative of a function and shows the working clearly step by step. It can be used to differentiate common algebraic expressions and understand how rules such as the power rule, sum rule, and other basic differentiation rules are applied. This makes it useful for checking answers, learning derivative methods, and practising calculus more confidently.

Step-by-step method

1. Set up the function.
2. Identify the main rule.
3. Split the expression if needed.
4. Work through each selected part using its own formula.
5. Combine the worked parts.
6. Simplify and write the final derivative.

Formula:

Example 1:

Step 1 – Set up the function.

In this problem: Write the function clearly before differentiating.

Step 2 – Identify the main rule.

In this problem: The main structure uses the sum/difference rule.

Step 3 – Split the expression term by term.

In this problem: The sum/difference rule says each term gets differentiated separately.

Step 4A – Select the next term from the sum.

In this problem: Work on this part by itself before combining it with the rest of the derivative.

Step 4B – Show the formula for this part.

In this problem: Use only the formula needed for this selected part.

Step 4C – Move the constant outside.

In this problem: The constant multiple rule keeps the coefficient in front of the derivative.

Step 4D – Show the formula for this part.

In this problem: Use only the formula needed for this selected part.

Step 4E – Apply the power rule.

In this problem: Multiply by the power and reduce the power by 1.

Step 4F – Multiply the constant by the x-part derivative.

In this problem: Now put the coefficient back with the derivative you just found.

Step 4G – Select the next term from the sum.

In this problem: Work on this part by itself before combining it with the rest of the derivative.

Step 4H – Show the formula for this part.

In this problem: Use only the formula needed for this selected part.

Step 4I – Move the constant outside.

In this problem: The constant multiple rule keeps the coefficient in front of the derivative.

Step 4J – Show the formula for this part.

In this problem: Use only the formula needed for this selected part.

Step 4K – Apply the variable rule.

In this problem: The derivative of x with respect to x is 1.

Step 4L – Multiply the constant by the x-part derivative.

In this problem: Now put the coefficient back with the derivative you just found.

Step 4M – Select the next term from the sum.

In this problem: Work on this part by itself before combining it with the rest of the derivative.

Step 4N – Show the formula for this part.

In this problem: Use only the formula needed for this selected part.

Step 4O – Apply the constant rule.

In this problem: A constant has derivative 0 because it does not change with x.

Step 5 – Combine the worked term derivatives.

In this problem: Now put every solved term derivative back into one expression.

Step 6 – Simplify and write the final derivative.

In this problem: Remove zero terms and combine like terms.

Final answer:

Example 2:

Step 1 – Set up the function.

In this problem: Write the function clearly before differentiating.

Step 2 – Identify the main rule.

In this problem: The main structure uses the sum/difference rule.

Step 3 – Split the expression term by term.

In this problem: The sum/difference rule says each term gets differentiated separately.

Step 4A – Select the next term from the sum.

In this problem: Work on this part by itself before combining it with the rest of the derivative.

Step 4B – Show the formula for this part.

In this problem: Use only the formula needed for this selected part.

Step 4C – Move the constant outside.

In this problem: The constant multiple rule keeps the coefficient in front of the derivative.

Step 4D – Show the formula for this part.

In this problem: Use only the formula needed for this selected part.

Step 4E – Apply the power rule.

In this problem: Multiply by the power and reduce the power by 1.

Step 4F – Multiply the constant by the x-part derivative.

In this problem: Now put the coefficient back with the derivative you just found.

Step 4G – Select the next term from the sum.

In this problem: Work on this part by itself before combining it with the rest of the derivative.

Step 4H – Show the formula for this part.

In this problem: Use only the formula needed for this selected part.

Step 4I – Apply the function rule.

In this problem: Differentiate the outside function, then multiply by du/dx.

Step 4J – Simplify this function derivative.

In this problem: Clean up this function result.

Step 5 – Combine the worked term derivatives.

In this problem: Now put every solved term derivative back into one expression.

Final answer: