chuffy said:Homework Statement
differentiate the following
y= x(x+2)(x+3)
Homework Equations
dy/dx
The Attempt at a Solution
The answer I'm given is dy/dx = 2x+5
Would this not be for (x+2)(x+3) = x2 +5x +6
dy/dx = 2x +5 +0
My problem is the x at the beginning of the brackets. Please help!
thanks
Differentiation is a mathematical process that involves finding the rate of change of a function with respect to its input variable. It is a fundamental concept in calculus and is used to analyze the behavior of functions.
Differentiation is used in science to model and understand the behavior of physical systems. It is particularly useful in fields such as physics, chemistry, and biology for analyzing rates of change, growth, and decay.
Simple differentiation refers to the process of finding the derivative of a function, while simplification involves reducing a complex expression into a simpler form. In simple differentiation, the goal is to find the instantaneous rate of change, while simplification aims to make a problem easier to solve.
One example of "confused - simple differentiation with simplification" could be a situation where a student is trying to find the derivative of a complex function, but they mistakenly simplify the expression before differentiating it. This can lead to incorrect results and confusion.
Some common mistakes when using "confused - simple differentiation with simplification" include forgetting to use the proper differentiation rules, simplifying the expression too early, and not carefully checking the final answer for accuracy. It is important to have a strong understanding of both differentiation and simplification in order to avoid these mistakes.