Finding the Second Derivative of a Cubic Function

Thread starter gr3g1
Start date Nov 5, 2005
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Derivative

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To find the second derivative of the cubic function y=(1-x^2)^3, the first derivative is correctly identified as -6x(1-x^2)^2. The discussion confirms that the product rule should be applied for differentiation, where u(x) is -6x and v(x) is (1-x^2)^2. The formula for the product rule is f'(x) = u'(x)v(x) + v'(x)u(x). This approach will lead to the correct calculation of the second derivative.

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
<br /> f(x)=u(x)v(x)<br />
then
<br /> f'(x) = u'(x)v(x) + v'(x)u(x)<br />
here u(x)=-6x and v(x)=(1-x^2)^2

Last edited: Nov 5, 2005

Nov 5, 2005

gr3g1

Thanks A lot

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