Derivative Calculator with Steps

Enter a function and get its derivative with a complete step-by-step solution. A live preview shows how your input is read; the calculator then names every differentiation rule it applies – product rule, quotient rule, chain rule and more – and explains each step, so you can follow the calculation and check your homework.

Examples – open the full step-by-step solution

How to enter functions

You want	Type	Example
Powers	`^`	`x^3`, `x^(1/3)`, `(2x+1)^5`
Multiplication	`*` (optional)	`3x` or `3x`, `xsin(x)`
Fractions	`/` with brackets	`(x+1)/(x-1)`
Roots	`sqrt()`	`sqrt(x^2+1)`
Exponential, logarithm	`e^`, `exp()`, `ln()` (`log()` = ln)	`e^(2x)`, `2^x`, `ln(x)`
Trigonometry	`sin cos tan cot sec csc`	`sin(x)^2`, `cos(3x)`
Inverse trig / hyperbolic	`arcsin arccos arctan`, `sinh cosh tanh asinh`	`arctan(x/2)`, `cosh(x)`

Choose the differentiation variable on the right if your function uses t, y or another letter – all other letters are treated as constants (partial derivative).

What is a derivative? 🤔

The derivative of a function is one of the most important concepts in calculus. Simply put, the derivative at a specific point describes the slope of the function’s graph exactly at that point. It tells us how much the function’s value changes when the input is varied slightly. With the derivative, denoted as $f'(x)$ or $\frac{d}{dx}f(x)$, we can analyze extrema, inflection points, and the overall monotonic behavior of functions.

How the derivative calculator works ⚙️

This calculator is more than just a tool for quickly finding results – it is designed as a learning aid to help you understand derivatives more easily.

Specifically developed for students and learners, it breaks down each function into its smallest logical parts and applies one differentiation rule per step. No steps are skipped: even basic derivatives like $\frac{d}{dx}(x) = 1$ and every simplification are shown, each with a short explanation and the changed part highlighted.

This way, you can dive into the often confusing topic of calculus even without deep prior knowledge and be well prepared for your next exam. 🎓

Every result is cross-checked with the computer algebra system Maxima, so you can rely on the final answer while you follow the steps.

The most important differentiation rules 📚

To differentiate more complex functions, you break them into simpler parts and apply basic rules. Our calculator supports these and many more, showing every step in detail.

Power Rule

Used for powers like $x^n$. The exponent becomes a factor and is then reduced by one.

$\frac{d}{dx}\left(u^{c}\right)=c\,u^{c-1}\,u'$

Sum/Difference Rule

Allows differentiating sums and differences term by term. Each part is handled separately.

$\frac{d}{dx}(u \pm v \pm \dots) = \frac{d}{dx}(u) \pm \frac{d}{dx}(v) \pm \dots$

Product Rule

Needed when two functions $u(x) \cdot v(x)$ are multiplied. The formula is $(u \cdot v)' = u'v + uv'$.

$\frac{d}{dx}(u \cdot v)=u'v+uv'$

Quotient Rule

The rule for differentiating quotients. Its structure is $\frac{u'v - uv'}{v^2}$.

$\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{u'v-uv'}{v^{2}}$

Chain Rule

The key rule for “nested” functions: differentiate the outer function and multiply by the derivative of the inner one.

$\frac{d}{dx}f(u)=f'(u)\cdot u'$

Exponential Rule

The derivative of the natural exponential $e^x$ is $e^x$ again. For a more complex exponent, the chain rule applies.

$\frac{d}{dx}(e^{u})=e^{u}\cdot u'$

Chain rule for the natural logarithm

The derivative of the natural logarithm $\ln(x)$ is $\frac{1}{x}$. For composed expressions, you need the chain rule.

$\frac{d}{dx}\big(\ln({u})\big) = \frac{u'}{{u}}$

Constant Factor Rule

A constant factor in front of a function is preserved during differentiation and multiplies the result.

$\frac{d}{dx}(c\,u)=c\,u'$

See all differentiation rules and the complete table of derivatives →

❓ Frequently asked questions

Is this derivative calculator free?

Yes. The calculator is free to use, needs no registration and shows the complete step-by-step solution for every function.

Does the calculator show the steps?

Yes. Each step names the differentiation rule that is applied (for example the product rule or the chain rule), shows the expression before and after the step and the simplified form. You can open the explanation of every rule from the step.

Which functions can I differentiate?

Polynomials, fractions, roots, powers with any exponent, $e^x$ and $a^x$, $\ln$ and $\log$, all trigonometric functions, inverse trigonometric functions (arcsin, arccos, arctan, …) and hyperbolic functions – also nested in any combination.

How do I get the second derivative?

Compute the first derivative and click Differentiate again below the result. The calculator then differentiates the result step by step.

Can I calculate partial derivatives?

Yes. Select the variable you want to differentiate with respect to (for example $y$). All other letters are treated as constants, which gives the partial derivative.

How can I share a solution?

Below every result you find Copy link to this solution. The link opens the same step-by-step solution again.