Chain Rule Calculator
Compute the derivative of a composite function using the chain rule. Enter f(u) and u(x) to get the derivative f'(x).
Published by:
isCalculator Editorial Team
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How to use this tool?
This calculator numerically computes the derivative of a composite function using the chain rule: f'(x) = f'(u(x)) · u'(x).
- Enter f(u) – the outer function in terms of
u. Example:u^2 + sin(u) - Enter u(x) – the inner function in terms of
x. Example:x^2 + 1 - Enter x value – the point at which to evaluate the derivative.
- Click Calculate Derivative.
Output: The numeric derivative at the given x, plus a step-by-step breakdown showing u(x), u'(x), f'(u), and the final product.
Tips:
- Use standard math syntax:
^for exponent,sin(x),cos(x),sqrt(x), etc. - All inputs are required. Invalid expressions will show an error message.
- The result uses numeric differentiation (central difference), so it's approximate but accurate for most practical purposes.
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Frequently Asked Questions
The chain rule is a formula to compute the derivative of a composite function. If h(x) = f(g(x)), then h'(x) = f'(g(x)) * g'(x).
You can use standard mathematical expressions with +, -, *, /, ^ (power), sin, cos, tan, exp, log, sqrt, etc. Use 'u' as variable in outer function and 'x' in inner function.
The calculator uses numeric differentiation with a small step size (1e-6) to approximate derivatives. It is accurate for most practical purposes.
