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Chain Rule Calculator

Step-by-step chain rule differentiation. Enter a composite function, select or identify the outer and inner functions, and get a fully worked solution with optional point evaluation.

Guided Chain Rule

Select the outer function type and define the inner function

Use x as the variable. Supported: +, -, *, /, ^, sqrt, sin, cos, ln, exp, etc.

Common Examples

Classic chain rule problems from calculus textbooks

Derivative

Step-by-Step Solution

Result

Enter a composite function
and click Differentiate

Chain Rule Formula

dy/dx = f'(g(x)) · g'(x)
Derivative of outer × derivative of inner
d/dx[f(g(x))] = f'(g(x)) · g'(x)

Common Derivatives f'(u)

uⁿn·uⁿ⁻¹
sin(u)cos(u)
cos(u)-sin(u)
tan(u)sec²(u)
eᵘeᵘ
ln(u)1/u
√u1/(2√u)
arcsin(u)1/√(1-u²)
arctan(u)1/(1+u²)
|u|u/|u|

Tips

🔁 Identify layers: The outermost operation is f, everything inside is g(x).

📐 Don't forget g'(x): Always multiply by the derivative of the inner function.

🔗 Triple chain: Add another factor for each nested layer: f'·g'·h'.

✅ Check units: Substitute g(x) back in place of u in the final answer.