Power rule
Differentiate x^4 - 3x^2 + 2
Method: Differentiate each term.
- 1Apply d(x^n)/dx = n x^(n-1) to each power.
- 2The derivative of the constant 2 is 0.
- 3Combine the resulting terms.
Final answer
Free online calculator
Derivative Calculator
Compute derivatives of polynomials, trigonometric, exponential, and logarithmic functions with detailed steps.
Derivative mode
Derivative
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How to Use the Derivative Calculator
1
Enter your function
Type any expression you want to differentiate.
2
Identify the operation
The solver detects the function and the independent variable.
3
Get the derivative
Receive the final answer plus a rule-by-rule explanation.
Example
How the Derivative Calculator Chooses a Method
Find a derivative and understand which differentiation rule applies at each stage.
The calculator classifies sums, products, quotients, powers, and compositions before applying the matching differentiation rules. The result is simplified and can be checked by differentiating equivalent forms or comparing numerical slopes.
Supported problem types
- Polynomial, rational, trigonometric, exponential, and logarithmic functions
- Product, quotient, and chain-rule combinations
- First and higher-order derivatives with respect to x
Limits and assumptions
- Piecewise functions and implicit equations may require a more explicit input format.
- A simplified symbolic answer can look different from an equivalent textbook form.
Worked Derivative Calculator Examples
Each example names the method, shows the ordered reasoning, and keeps the final answer separate so you can check your own work.
Product rule
Differentiate x^2 sin(x)
Method: Use (uv)' = u'v + uv'.
- 1Let u=x^2 and v=sin(x).
- 2Compute u'=2x and v'=cos(x).
- 3Substitute into the product rule.
Final answer
Chain rule
Differentiate e^(3x^2)
Method: Differentiate the outer exponential and then the inner exponent.
- 1Set u=3x^2.
- 2The outer derivative is e^u and du/dx=6x.
- 3Multiply the outer and inner derivatives.
Final answer
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What the Derivative Calculator Helps You Understand
Compute derivatives of polynomials, trigonometric, exponential, and logarithmic functions with detailed steps.
Learning focus 1
Type any expression you want to differentiate.
Learning focus 2
The solver detects the function and the independent variable.
Learning focus 3
Receive the final answer plus a rule-by-rule explanation.
Input tips
- • Type any expression you want to differentiate.
- • Yes. You can compute derivatives and view step-by-step explanations at no cost.
Common mistakes to avoid
- • Applying the power rule to a product without the product rule.
- • Forgetting the inner derivative when using the chain rule.
Frequently Asked Questions
Is this derivative calculator free?
Yes. You can compute derivatives and view step-by-step explanations at no cost.
Can I see the differentiation rules used?
Each step lists the rule applied, such as power rule, product rule, or chain rule.
How should I enter a composite function?
Use parentheses around the inner expression, for example exp(3*x^2) or sin(x^2+1).
How can I check a derivative?
Differentiate an equivalent form, inspect the rules used, or compare the result with numerical slopes at valid sample points.