Calculus
Class 12

Chain Rule

ddx[f(g(x))]=f(ˊg(x))g(ˊx)\frac{d}{dx}[f(g(x))] = f\'(g(x)) \cdot g\'(x)
0123456−2−1.5−1−0.500.511.52
d/dx[f(g(x))] = f'(g(x)) × g'(x)

Adjust Variables

Inner coeff
a =
15

For composite functions, multiply the outer derivative by the inner derivative. Essential for differentiating nested functions.

Real-World Applications

Physics — Velocity of projectile: d/dt(height(time)) requires chain rule.

Machine learning — Backpropagation in neural networks is chain rule applied.

Economics — Elasticity calculations: (dQ/dP)(P/Q).

Biology — Population change through dependent factors.

Engineering — Sensitivity analysis in cascaded systems.

Finance — Option Greeks like Delta and Gamma.

Chemistry — Related rates in chemical kinetics.

Robotics — Jacobian matrix calculations.

Signal processing — Filter cascade analysis.

Computer graphics — Hierarchical transformations.

Community Explanations

No community explanations yet. Be the first to share yours!

to write your own explanation

Community Aha! Moments

to share your insights

No insights yet. Be the first to share!

Related Formulas