In calculus, differentiating a function means finding its derivative, which tells you how fast the function is changing at a specific point. Geometrically, it gives the slope of the curve’s tangent line at that point, and physically it often represents an instantaneous rate of change like velocity.

Simple idea

If y=f(x)y=f(x)y=f(x), then differentiating finds f′(x)f'(x)f′(x) or dydx\frac{dy}{dx}dxdy​, which measures how much yyy changes when xxx changes a tiny amount. In plain language, it answers: “If I nudge xxx a little, how does yyy respond?”

Why it matters

Differentiation is used to find slopes, speeds, acceleration, and points where a function has a maximum or minimum. It is one of the main tools in calculus because it turns a curve into a precise description of change.

Tiny example

For f(x)=x2f(x)=x^2f(x)=x2, differentiating gives f′(x)=2xf'(x)=2xf′(x)=2x, which means the slope gets steeper as xxx increases. So at x=3x=3x=3, the slope is 666, and at x=1x=1x=1, the slope is 222.

One-line definition

Differentiating in calculus is the process of finding the derivative so you can measure instantaneous change and tangent-line slope.