What is the derivative of x squared?

The derivative of x squared is 2x using the power rule.

Why do I need to use asterisk for multiplication?

The parser requires explicit multiplication such as 3*x instead of 3x.

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Calculus & Math

Derivative Calculator

Q: How do I find the derivative of a function?

Enter your function, choose the variable, and click Calculate to get the symbolic derivative.

Q: Can this calculator find second and third derivatives?

Absolutely! You can easily calculate higher derivatives by selecting an order between 2 and 10.

Free online derivative calculator — compute first, second, and higher-order derivatives symbolically. It helps to calculate polynomials, trig, exponential etc. Ideal for calculus students and engineers.

Symbolic results powered by math.js. For exam or homework, verify steps manually.

Enter your function

f(x) =

Tip: use * for multiplication — e.g. 3*x, not 3x

Variable

Derivative order

Simplify

Evaluate at

Enter a function and click Calculate derivative, or use an example above.

Calculation history

No calculations yet.

Derivative rules

Quick reference for common differentiation rules.

Power rule

d/dx xⁿ = n·xⁿ⁻¹

Constant

d/dx c = 0

Sum rule

(f + g)′ = f′ + g′

Product rule

(fg)′ = f′g + fg′

Quotient rule

(f/g)′ = (f′g − fg′)/g²

Chain rule

d/dx f(g(x)) = f′(g(x))·g′(x)

sin(x)

cos(x)

−sin(x)

tan(x)

sec²(x)

eˣ

ln(x)

1/x

aˣ

aˣ · ln(a)

arcsin(x)

1/√(1−x²)

arctan(x)

1/(1+x²)

sinh(x)

cosh(x)

sinh(x)

Input syntax

Multiplication

3*x or 3 * x

Power

x^2, x^(1/3)

Euler's number

e or E

Square root

sqrt(x)

Absolute value

abs(x)

What Is a Derivative?

In physics, derivatives describe velocity (derivative of position) and acceleration (derivative of velocity).

"f′(x) = lim_h→0 [f(x + h) − f(x)] / h"

Common derivative examples

d/dx (x³) = 3x² — power rule
d/dx (sin x) = cos x
d/dx (eˣ) = eˣ
d/dx (ln x) = 1/x
d/dx (x² · sin x) = 2x·sin x + x²·cos x — product rule

When to use a derivative calculator

Checking homework in Calculus I & II (differentiation rules)
Finding critical points for optimization problems
Computing second derivatives for concavity and inflection points
Evaluating derivatives at a specific point for tangent-line equations

Related calculus tools

Derivative Calculator FAQ

How do I find the derivative of a function?

Enter your function f(x), choose the variable, and click Calculate. The calculator applies differentiation rules symbolically — power rule, product rule, chain rule, and trig/log rules — to return f′(x).

What is the derivative of x²?

d/dx (x²) = 2x. In general, d/dx (xⁿ) = n·xⁿ⁻¹.

Can this calculator find second and third derivatives?

Yes. Set order between 2 and 10. The tool differentiates repeatedly and shows intermediate steps when order > 1.

Why do I need to use * for multiplication?

The parser requires explicit multiplication. Write 3*x instead of 3x, and 2*sin(x) instead of 2sin(x). Use ^ for exponents: x^3.

What is the difference between a derivative and an integral?

An integral finds accumulated area under a curve. They are inverse operations — the fundamental theorem of calculus links them.

How do I evaluate a derivative at a specific point?

Enter a number in the Evaluate at field (e.g. 2). After computing f′(x), the calculator substitutes that value and shows the numeric result f′(2).

Math

Calculate the derivative of a function with respect to a variable instantly. Derivatives are essential in calculus, physics, and engineering to determine rates of change. Simply input your function, and this calculator provides accurate results, supporting tasks in advanced mathematics, economics, and science.

Derivative Calculator – it simplifies complex calculations.

Do you know, derivatives are the building Block calculators, which is the measuring of change in a given variable due to change in another variable. Calculating derivatives can be tough, whether you are a student, a teacher, or a professional. That’s where our Derivative Calculator comes into play, offering step-by-step solutions to derive derivatives with ease.

Our Derivative Calculator will give you accurate results in no time!

Important Features of Our Derivative Calculator

Partial Derivative Calculator
Easily partial derive multivariable functions. This calculator will help you understand how to find the partial derivatives of a multivariable function step-wise.
Derivative Calculator with Steps, and much more
Understanding in detail about how derivatives are calculated. This is a great tool to learn and check your calculations.
Second Derivative Calculator
Are you needing to find the second derivative to study a function for concavity or for acceleration?
Third Derivative Calculator
Our tool to finds third-order derivative in advanced calculus problems saves the time and effort needed to find it manually.
Derivative of x
Our intuitive calculator has our Simple Calculator, allowing you to compute the derivative of any function involving xxx, simple or complex.
dy/dx Calculator
Use your computer power to easily find derivatives explicitly with respect to dy/dx(1)dy/dx(1)dy/dx(1) in the name of single-variable functions.
Logarithmic Difference Calculator
Easily solve logarithmic differentiation problems, great for dealing with exponential, composite functions.
Numerical Derivative Calculator
Our calculator returns accurate numerical outcomes for approximate derivatives or in those cases where analytical solutions are not feasible.

Why Our Derivative Calculator?

User-friendly interface.
For example, allows for many types of differentiation.
Copious amounts of examples with step-by-step solutions to facilitate learning.
You can perform both basic and pretty complicated calculus problems.

FA Questions of Otten (FAQs)

Q: What’s a derivative calculator?

A: A derivative calculator helps in determining how a function changes as its input variable changes. It makes things a lot easier, particularly for complicated equations, and provides step-by-step solutions.

Q: What is the method for the partial derivative calculator?

A: Write a multivariable function and tell it which variable to differentiate with respect to. The calculator will calculate the partial derivative and show work.

Q: Does the calculator do higher-order derivatives?

A: Yes, The Second Derivative Calculator or Third Derivative Calculator are available to determine higher derivatives.

Q: Will the calculator do logarithmic differentiation?

A: Absolutely! If you are ever in a situation like this ever, our Logarithmic Differentiation Calculator is made for you!

Q: Define numerical differentiation.

A: Numerical differentiation is the numerical approach to compute the derivative of a function given that the function does not allow for an analytic method to solve for the derivative. With our Numerical Derivative Calculator, you can calculate accurate results.

So, to brush your concepts of calculus problem solving you can try our Derivative Calculator.

Derivative Examples

1. \( f(x) = x^2 \)

Solution: \( f'(x) = 2x \)

2. \( f(x) = e^x \)

Solution: \( f'(x) = e^x \)

3. \( f(x) = \sin(x) \)

Solution: \( f'(x) = \cos(x) \)

4. \( f(x) = \cos(x) \)

Solution: \( f'(x) = -\sin(x) \)

5. \( f(x) = \ln(x) \)

Solution: \( f'(x) = \frac{1}{x} \)

6. \( f(x) = x^3 \)

Solution: \( f'(x) = 3x^2 \)

7. \( f(x) = \tan(x) \)

Solution: \( f'(x) = \sec^2(x) \)

8. \( f(x) = \sqrt{x} \)

Solution: \( f'(x) = \frac{1}{2\sqrt{x}} \)

9. \( f(x) = \frac{1}{x} \)

Solution: \( f'(x) = -\frac{1}{x^2} \)

10. \( f(x) = \ln(\sin(x)) \)

Solution: \( f'(x) = \cot(x) \)

Published

2025-09-23 23:13:28

Updated

0000-00-00 00:00:00

Author

Taylor Bennett