- #1
SciGuy26
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Homework Equations
Take the second derivative of:
cos(x^2)
The Attempt at a Solution
cos(x^2)
dy/du = -sin(u)
du/dx = 2x
dy/dx= -2xsin(x^2)
I don't know how to begin taking the derivative of this a second time...
Differentiation is a mathematical process used to find the rate of change or slope of a function at a specific point. It is also known as finding the derivative of a function.
The purpose of differentiation is to help us understand the behavior of a function and how it changes over time or in response to varying inputs. It is also used to solve optimization problems and to find the maximum or minimum values of a function.
Differentiation is the process of finding the rate of change of a function, while integration is the process of finding the area under a curve. In other words, differentiation helps us find the slope of a function, while integration helps us find the total change over a given interval.
The basic rules of differentiation include the power rule, product rule, quotient rule, and chain rule. These rules help us find the derivative of more complex functions by breaking them down into simpler parts and applying specific formulas.
Differentiation is used in a variety of fields, including physics, economics, engineering, and statistics. It is used to model and predict the behavior of systems, to optimize processes, and to analyze data. Some common applications include calculating speed and acceleration, finding the maximum profit for a business, and predicting the growth of a population over time.