Finding the Second Derivative of a Cubic Function

Thread starter gr3g1
Start date Nov 5, 2005
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Derivative

In summary, a high order derivative is a mathematical concept that represents the rate of change of a function at a specific point in its domain. They are important because they provide more detailed information about the behavior of a function, such as curvature and concavity. To find high order derivatives, one can use various calculus rules. They have many real-life applications and understanding them can be improved through a strong understanding of basic calculus concepts and practice.

Nov 5, 2005

gr3g1

Hey guys,

My function is : y=(1-x^2)^3
I found my first derivative as : -6x(1-x^2)^2
But i can't seem to find the second derivative.

Do I use the product rule?

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Nov 5, 2005

gdumont

You are right use the product rule
[tex]
f(x)=u(x)v(x)
[/tex]
then
[tex]
f'(x) = u'(x)v(x) + v'(x)u(x)
[/tex]
here [itex]u(x)=-6x[/itex] and [itex]v(x)=(1-x^2)^2[/itex]

Last edited: Nov 5, 2005

Nov 5, 2005

gr3g1

Thanks A lot

FAQ: Finding the Second Derivative of a Cubic Function

What is a high order derivative?

A high order derivative is a mathematical concept that represents the rate of change of a function at a specific point in its domain. It is the derivative of a derivative and can be thought of as the rate of change of the rate of change.

Why are high order derivatives important?

High order derivatives are important because they allow us to analyze the behavior of a function in greater detail. They provide information about the curvature and concavity of a function, which can help us understand its behavior and make predictions.

How do you find high order derivatives?

To find high order derivatives, you can use the power rule, product rule, quotient rule, or chain rule, depending on the complexity of the function. You may need to apply these rules multiple times to find the desired derivative.

What are some real-life applications of high order derivatives?

High order derivatives have many real-life applications, such as in physics, engineering, economics, and statistics. For example, they can be used to model the motion of objects, analyze the stability of systems, and optimize functions in various fields.

How can I improve my understanding of high order derivatives?

To improve your understanding of high order derivatives, it is important to have a strong grasp of basic calculus concepts, such as limits, derivatives, and integrals. You can also practice solving problems and working with different types of functions to develop your skills and intuition.