Derivative Calculator with Steps
Type a function and Calvo differentiates it step by step, naming every rule it uses. Choose the 2nd, 3rd or 4th derivative, or evaluate the derivative at a point.
Differentiate step by step
Type * for multiplication (2x and x sin x also work), ^ for powers, sqrt(), ln() for natural log, log() for base 10, e^x or exp(x). Write sin(x), cos(x), tan(x), arcsin(x), arctan(x) and so on.
Differentiation rules used
| Rule | Formula |
|---|---|
| Power rule | d/dx[xn] = n·xn−1 |
| Constant multiple | d/dx[c·f] = c·f′ |
| Sum / difference | (f ± g)′ = f′ ± g′ |
| Product rule | (uv)′ = u′v + uv′ |
| Quotient rule | (u/v)′ = (u′v − uv′) / v² |
| Chain rule | d/dx[f(g(x))] = f′(g(x))·g′(x) |
| Exponential / log | (ex)′ = ex, (ax)′ = axln a, (ln x)′ = 1/x |
| Trigonometric | (sin x)′ = cos x, (cos x)′ = −sin x, (tan x)′ = sec²x |
Worked example: product and chain rule
Find d/dx[x² sin x]. Take u = x² and v = sin x. Then u′ = 2x and v′ = cos x. By the product rule, the derivative is u′v + uv′ = 2x sin x + x² cos x.
For a composite function such as sin(3x²), the chain rule gives cos(3x²)·6x = 6x cos(3x²).
How Calvo checks the answer
Calvo differentiates with exact fractions, writes each rule it uses, simplifies, and then compares the answer with a numerical derivative at several points. The answer is only shown when they agree, and you will see a “verified” mark next to it.
Limits
The solver works with one variable. If you type another letter along with x, it is treated as a constant. Functions with absolute value or piecewise definitions are not supported.
FAQ
How do I find a derivative step by step?
Identify the rule: power, product, quotient or chain. Apply it, differentiate each piece, then simplify. Calvo writes every rule it applies and the value it finds.
What is the derivative of x^2 sin x?
By the product rule it is 2x sin x + x^2 cos x.
When do I use the chain rule?
Use it when a function sits inside another, like sin(3x^2), e^(2x) or (x^2+1)^5. Differentiate the outer function, keep the inside, then multiply by the derivative of the inside.
Does it give the second or third derivative?
Yes. Choose the order in the box. Calvo differentiates the simplified result again for each order.
Can I find the derivative at a point?
Yes. Put a value such as 2 or pi in the At x box and Calvo evaluates the derivative there.
What does log mean here?
log(x) is base 10 and ln(x) is the natural logarithm. d/dx[log x] = 1/(x ln 10).
Is the answer always simplified?
Calvo simplifies like terms and powers, but a textbook may present an equivalent form that looks different. Both are correct if they are equal.
Does it work offline?
Yes. The calculation runs in your browser and the page is cached after your first visit.