Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
Differentiation is the process of finding the derivative of a function, which measures how a function's output changes as its input changes. It provides the slope of the tangent line to the function at any given point.
5 Must Know Facts For Your Next Test
The derivative of a function $f(x)$ at a point $x$ is denoted as $f'(x)$ or $\frac{df}{dx}$.
The power rule for differentiation states that if $f(x) = x^n$, then $f'(x) = nx^{n-1}$.
The derivative represents the instantaneous rate of change of the function with respect to its variable.
Common differentiation rules include the product rule, quotient rule, and chain rule.
If a function is differentiable at a point, it must also be continuous at that point.
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Related terms
Derivative: A measure of how a function's output value changes as its input value changes. Denoted by $f'(x)$ or $\frac{dy}{dx}$.
Product Rule: A formula used to find the derivatives of products of two functions: $(fg)' = f'g + fg'$.
Chain Rule: A formula for computing the derivative of the composition of two or more functions: $(f(g(x)))' = f'(g(x))g'(x)$.