Formula Used
The power rule is one of the fastest derivative rules.
It works on a term written as ax^n.
The letter a is the coefficient.
The letter n is the power.
The formula is d/dx(ax^n) = anx^(n-1).
The coefficient is multiplied by the power.
Then the power is reduced by one.
Constants use a separate rule.
The derivative of any constant is zero.
How To Use This Calculator
Type a power expression in the input box.
Use terms such as 6x^5, -4x^3, or 7x.
Add or subtract terms as needed.
Choose the variable letter used in your expression.
Enter an optional value for the variable.
The tool can then evaluate the derivative at that point.
Select decimal places for rounded output.
Choose a result style.
Press the submit button.
The answer appears above the form.
Use the CSV or PDF button to save the work.
About The Power Rule Method
A derivative measures a rate of change. In algebra and calculus, many functions are built from powers. The power rule handles those powers directly. It is useful for polynomial terms. It also works with fractional powers. It can handle negative powers too. This makes it flexible for many school and engineering problems. The calculator reads each term separately. It identifies the coefficient and exponent. It then applies the rule to that single term. After all terms are processed, the tool combines matching powers when selected.
Why Step Output Helps
A final derivative is useful. Clear steps are better for learning. Each row shows the original term. It also shows the old coefficient and old power. The new coefficient is found by multiplication. The new power is one less than before. This structure helps users check mistakes. It also helps compare manual work with the computed result. If a constant is entered, the table shows zero. That makes the constant rule easy to remember.
Supported Input Ideas
You can enter simple polynomials.
You can enter decimal coefficients.
You can enter fractional coefficients like 3/4x^2.
You can enter negative powers like x^-3.
You can enter decimal powers like x^0.5.
Keep multiplication simple.
Use one variable in the expression.
Avoid parentheses and products between variables.
The purpose is focused.
It solves expressions that fit the direct power rule.
For product, quotient, or chain rule work, rewrite the expression first when possible.
Practical Uses
Students can use this calculator for homework checks. Teachers can use it to make examples. Tutors can use it to explain each term. Analysts can use it for quick symbolic changes. The export options are helpful for records. CSV files open in spreadsheet software. PDF files are easier to share. The calculator stays simple, but it includes advanced choices. It gives symbolic answers, numerical evaluations, steps, and tables. That makes it useful for both practice and review.