SL 5.6—Differentiating polynomials n E Q. Chain, product and quotient rules

Differentiation is one of the most powerful tools in calculus. At its core, it measures the rate of change of a function , telling us how quickly (and in which direction) a function's output changes as its input changes.

Derivative: The derivative of a function $f(x)$, written $f^{\prime }(x)$ or $\frac{dy}{dx}$, gives the instantaneous rate of change of $f$ at any point $x$. Geometrically, it represents the gradient of the tangent line to the curve at that point.

In SL 5.6, we build our differentiation toolkit with four key techniques:

• The power rule (for polynomials with rational exponents)
• The chain rule (for composite functions)
• The product rule (for products of two functions)
• The quotient rule (for quotients of two functions)

Mastering these rules , and knowing when to combine them , is essential for success in IB DP Analysis & Approaches.