Calculus
Class 11

Power Rule

ddx(xn)=nxn1\frac{d}{dx}(x^n) = nx^{n-1}
0123450246810
d/dx(xⁿ) = n×x^(n-1)

Adjust Variables

Exponent n
n =
15

The most fundamental differentiation rule. Works for any real exponent n, including fractions and negatives.

Real-World Applications

Physics — Deriving v = dx/dt and a = dv/dt for polynomial motion.

Economics — Marginal analysis of polynomial cost/revenue functions.

Engineering — Polynomial curve fitting and slope analysis.

Biology — Growth rate in polynomial population models.

Finance — Rate of return on polynomial investment growth.

Chemistry — Rate of concentration change in reactions.

Statistics — Derivative of polynomial regression models.

Computer graphics — Bezier curve tangent calculations.

Machine learning — Gradient descent optimization.

Signal processing — Polynomial filter response analysis.

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