Calculate derivatives instantly
This derivada online calculator helps you find the first and second derivative of a function in seconds. Type your function, click Calculate Derivative, and you get symbolic results immediately. If you provide a point value, the tool also computes the slope at that point.
It is useful for students, teachers, engineers, and anyone reviewing calculus. You can test polynomial, trigonometric, logarithmic, exponential, and rational expressions quickly without manual algebra mistakes.
How to use this derivative calculator
1) Enter a function
Write your function with standard calculator syntax. Use * for multiplication and ^ for powers.
For example: 3*x^4 - 5*x + 2.
2) Choose the variable
Most problems use x, but you can use t, y, or another variable if needed.
3) (Optional) Evaluate at a point
Add a numeric value to find both f(a) and f'(a), where a is the point you entered.
Supported function types
- Polynomials:
x^5 - 4*x^2 + x - Trigonometric:
sin(x),cos(x),tan(x) - Exponential:
e^x,2^x - Logarithmic:
ln(x),log(x) - Mixed expressions:
sin(x)*x^2 + ln(x) - Fractions:
(x^2+1)/(x-3)
Core derivative rules (quick refresher)
Power rule
If f(x)=x^n, then f'(x)=n*x^(n-1).
Product rule
If f(x)=u(x)*v(x), then f'(x)=u'(x)*v(x)+u(x)*v'(x).
Quotient rule
If f(x)=u(x)/v(x), then f'(x)=(u'v-uv')/v^2.
Chain rule
If f(x)=g(h(x)), then f'(x)=g'(h(x))*h'(x).
Common input tips
- Use parentheses clearly:
sin(x^2)is different from(sin(x))^2. - Write logarithms as
ln(x)for natural log. - Use decimal points for constants when needed (e.g.,
2.5*x). - If your function includes division, wrap numerator/denominator in parentheses.
Why this tool is useful for learning
A good derivative calculator does more than give an answer. It helps you check homework, verify lecture notes, and build intuition about rate of change. You can compare your manual result with the calculator output and quickly identify where your simplification or rule application went wrong.
For exam prep, this is especially useful: test many function forms in a short session and become faster with derivative patterns.
Frequently asked questions
Does it compute higher-order derivatives?
Yes. This page shows both first and second derivatives automatically.
Can I evaluate derivatives at a specific point?
Yes. Enter a value in the optional point field to calculate the function value and slope there.
What if I get an error?
Usually the expression has a syntax issue. Check parentheses, multiplication signs, and function names. Then try again.