Derivative Calculator
Symbolic differentiation — powers, trig, eˣ and ln
f(x)
Terms: x^n, x, constants, sin(x) cos(x) tan(x) sec(x) csc(x) cot(x), e^x, ln(x), 1/x, sqrt(x)
d/dx ( )
=
Derivative Calculator — Complete Guide & Instructions
MakeCard Derivative Calculator differentiates a function of x symbolically and returns a clean simplified result. It parses sums of terms covering powers, trigonometric functions, exponentials, logarithms, reciprocals, and square roots — the bread and butter of first-year calculus. Students checking homework and engineers needing a quick derivative both get an instant answer.
How to Use Derivative Calculator
- 1 Type the function into the f(x) field — for example 3x^2 + 2x - 5 + sin(x), or press Sample for a demo.
- 2 Use plain syntax: x^n for powers, sin(x) cos(x) tan(x) sec(x) csc(x) cot(x), e^x, ln(x), 1/x, sqrt(x).
- 3 Press Differentiate.
- 4 Read the result shown as d/dx of your input.
Key Features & Capabilities
- Power rule for x^n terms including fractional and negative exponents.
- All six trigonometric derivatives — sin, cos, tan, sec, csc, cot.
- Exponential e^x and natural logarithm ln(x) handled symbolically.
- 1/x and sqrt(x) rewritten as powers and differentiated correctly.
- Constant coefficients and term-by-term sums supported.
- Sample button loads a worked example instantly.
Supported Formats & Specifications
| Parameter | Specification |
|---|---|
| Input syntax | Sum of terms — 3x^2, 2x, -5, sin(x), e^x, ln(x), 1/x, sqrt(x) |
| Supported functions | x^n, x, constants, sin cos tan sec csc cot, e^x, ln(x), 1/x, sqrt(x) |
| Output | Simplified symbolic derivative d/dx |
Practical Everyday Use Cases
- Checking calculus homework answers for polynomial and trig derivatives.
- Finding slope functions for physics motion problems.
- Verifying marginal cost or rate-of-change expressions quickly.
- Practising term-by-term differentiation before exams.
Pro Tips for Best Results
- Write powers as x^2, x^3 — coefficients like 3x^2 need no multiplication sign.
- For products like x·sin(x), expand or differentiate manually — this solver works term-by-term, not product/chain rule.
- Use sqrt(x) and 1/x directly; they are treated as x^0.5 and x^-1 internally.
Common Problems & Solutions
Check spelling and syntax — write sin(x) not sin x, x^2 not x², and keep the variable as lowercase x.
The tool differentiates sums of terms only; products, quotients, and nested functions need the product, quotient, or chain rule applied manually first.
Privacy & Security
100% Client-Side Execution
Your function is parsed and differentiated inside the browser — no expressions are sent to a server.
Frequently Asked Questions
Everything you need to know about using Derivative Calculator
Type the function using x^n, sin(x), e^x, ln(x) style syntax and press Differentiate — the symbolic result appears instantly.
cos(x) — and this tool shows it along with derivatives of cos, tan, sec, csc, and cot for any term you enter.
No — it differentiates sums of simple terms (powers, trig, exponentials, logs). Composite functions like sin(2x) need manual rewriting first.
e^x — the exponential function is its own derivative, which is why it appears so often in calculus problems.
Related FreeToolsBazaar Tools
Ready to Use Derivative Calculator?
100% free, browser-based, and private. No installation, registration, or file upload to external servers required.
Start Using Derivative Calculator