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𝑓′ Derivative Calculator

Differentiate polynomial functions of x symbolically using the power rule. View f'(x), simplifications, and evaluation at a specific x value with clear, step-by-step working.

Derivative Calculator

Differentiate single‑variable polynomial functions step by step. Enter an expression in x, see the symbolic derivative using the power rule, and optionally evaluate it at a specific x‑value.

Function

f(x)

Supports polynomials like 4x^3 - 2x + 7. Use x as the variable and ^ for powers.

Uses power rule d/dx [a x^n] = n·a x^(n−1)Orders terms from highest to lowest power

Evaluate derivative at a point

x value

Leave blank if you only want the symbolic derivative.

Result

f'(x)

6x + 2

f'(1)

Step‑by‑step working

For 3x^2, use power rule: d/dx [a x^n] = n · a x^(n−1). Here a = 3, n = 2, so derivative is 6x^1.
For 2x, use power rule: d/dx [a x^n] = n · a x^(n−1). Here a = 2, n = 1, so derivative is 2x^0.
d/dx of constant -5 is 0.

How to use this tool

Write your function as a polynomial in x with powers using ^, like 4x^3 - 2x + 7.
Read through the symbolic derivative f'(x) and each power‑rule differentiation step.
Optionally plug in an x value to see the slope or gradient at that point.

Perfect online derivative calculator for calculus homework

Use this derivative calculator to check manual differentiation of polynomials in seconds.
See a plain‑English explanation for each term’s derivative using the power rule.
Use the evaluation feature to understand slopes of tangent lines and gradients at specific x values.

What this derivative calculator supports

Polynomial expressions in x composed of constants and terms like 3x^2, -4x, or 7.
Any real coefficients and whole‑number powers using the standard power rule.
Automatic ordering and simplification of the derivative for clean final answers.

FAQ

Does this step‑by‑step derivative calculator handle trig functions or ln(x)?: This version focuses on polynomial functions of x. For trig, exponentials, and logs, consider rewriting into polynomial form where possible or use the scientific calculator for numeric checks.
Can I use a different variable instead of x in the derivative calculator?: The parser expects x as the variable. If your problem uses another letter, substitute x in its place when typing the expression.
What happens with fractional or negative powers?: Non‑integer powers are not fully supported in this symbolic derivative tool. Stick to whole‑number exponents for reliable step‑by‑step working.

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