Discover the product rule, a fundamental technique for finding the derivative of a function expressed as a product of two functions. We'll learn how to apply this rule to simplify differentiation and enhance our understanding of calculus.
Review your knowledge of the Product rule for derivatives, and use it to solve problems.
We explore the product rule by finding the derivative of eˣcos(x). We identify eˣ as the first function and cos(x) as the second, then apply the product rule to calculate the derivative, simplifying our result for a clearer understanding.
We explore how to evaluate the derivative of the product of two functions, f(x) and h(x), at x=3, using given values for f, h, and their derivatives. Applying the product rule, we calculate the derivative of f(x)⋅h(x) at x=3 with ease.
The derivative of a function describes the function's instantaneous rate of change at a certain point - it gives us the slope of the line tangent to the function's graph at that point. See how we define the derivative using limits, and learn to find derivatives quickly with the very useful power, product, and quotient rules.
The product rule tells us how to find the derivative of the product of two functions:
Let's explore how to break down complex expressions and determine the right derivative rules to apply. We'll learn how to identify the structure of these expressions and decide the order of operations, using the chain rule and product rule. This strategy will help us tackle even the most elaborate expressions with confidence.
👉 Learn how to find the derivative of a function using the product rule. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the variable ...