Maths / Calculus
Derivative Calculator with Step-by-step Working
Find first to fifth derivatives in one variable. See power, product, quotient and chain rules, check a point, and compare the function with its first derivative.
Derivative Calculator with Step-by-step Working: Type a function and get its first to fifth derivative with each step explained: which rule applies (power, product, quotient or chain rule) and what it gives. The answer is double-checked by a second, independent method before it is shown; you can evaluate it at a point and plot the function with its first derivative. Runs 100% locally in your browser with zero server file uploads.
- Category
- School & study tools
- Runs
- In your browser
- Cost
- Free · no sign-up
- Availability
- Ready to use
Runs entirely in your browser
Real-valued expressions in one variable. Up to 512 characters. Infinite bounds, singular intervals and general piecewise expressions are unsupported.
Differentiation rules
For a product uv, use u′v + uv′. For a quotient u/v, use (u′v − uv′)/v² where v is nonzero. For a composition f(g(x)), multiply f′(g(x)) by g′(x). Each working line is generated from the parsed tree.
OpenStax Calculus Volume 1, Chapter 3: https://openstax.org/books/calculus-volume-1/pages/3-introduction
Domain and verification
This is real, single-variable calculus. General piecewise functions, additional symbolic parameters and expressions over the size limit are unsupported. The graph samples a finite window and may miss narrow features.
Use the scientific calculator for arithmetic, the graphing calculator for a larger graph, or the quadratic equation solver for quadratic roots.
Nerdamer 2.0.0 is distributed under Apache-2.0. Documentation: https://nerdamer.com/documentation
How to use it
- Enter an expression and check the live parsed preview.
- Choose the variable, angle unit, derivative order and an optional point.
- Calculate, then read the result, cross-check and named rules.
Privacy & limitations
Calculations run in your browser. Expressions are not uploaded.
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Frequently asked questions
Which input notation is supported?
Use x^2, sin(x), e^x, ln(x), sqrt(x), |x|, log_2(x) or log(x,2). Implicit multiplication such as 2x and 3sin(x) is supported. Multiplication and division have equal precedence, so write 1/(2x) explicitly.
What changes in degrees?
Trig arguments are multiplied by pi/180; inverse trig outputs by 180/pi. Those conversion factors also enter the derivatives. Radians are the default.
Is the cross-check a proof?
Simplification to zero is a symbolic check on the applicable domain. Seven matching random numerical points are supporting evidence, not a proof. The original expression domain still applies.
What happens at an absolute-value corner?
The rule is x/|x| away from zero. The calculator does not infer a derivative at the corner, even if a later simplification cancels terms.
Free tool · runs in your browser · no account required