Calculadora de Regra da Cadeia
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
(f ∘ g)'(x) = f'(g(x)) · g'(x)
About this calculator
The Chain Rule Calculator solves derivatives of composite functions, i.e., functions of the form f(g(x)). It computes the derivative of the composition using the formula (f ∘ g)'(x) = f'(g(x)) · g'(x). To use it, you need to provide two expressions: the derivative of the outer function evaluated at the inner function, f'(g(x)), and the derivative of the inner function, g'(x). The result is the product of these two derivatives.
This tool is useful for calculus students learning the chain rule. Instead of doing the entire process manually, you can verify your calculations or get the result quickly. For example, to differentiate sin(x²), you enter f'(g(x)) = cos(x²) and g'(x) = 2x, and the calculator returns cos(x²) · 2x.
Cautions: ensure the expressions are entered correctly. f'(g(x)) must be the derivative of the outer function f evaluated at g(x), not the derivative of f with respect to x. Also, the tool does not simplify the result; it only multiplies the two provided expressions. Use appropriate parentheses to avoid ambiguity.
Frequently asked questions
Do I need to type the original function or just the derivatives?
Just the derivatives f'(g(x)) and g'(x). The calculator does not take the original function f(g(x)), only the two partial derivatives.
Is the result simplified?
No. The calculator only multiplies the two provided expressions, without simplifying. You may need to simplify manually.
Can I use this calculator for higher-order derivatives?
No. It only computes the first derivative (first-order derivative) of composite functions.
What if my function has more than two compositions?
Apply the chain rule repeatedly. You can use the calculator for each step, but it only accepts two functions at a time.
Does the calculator accept trigonometric or logarithmic functions?
Yes, as long as you enter the correct derivatives. For example, for ln(sin(x)), enter f'(g(x)) = 1/sin(x) and g'(x) = cos(x).