# What is the second derivative of #f(x)=cos(-1/x^3) #?

For second derivative, we use the formula of product derivatives i.e.

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The second derivative of ( f(x) = \cos(-1/x^3) ) is ( f''(x) = \frac{6 \cos(1/x^3)}{x^7} - \frac{54 \sin(1/x^3)}{x^10} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- How do you determine the intervals where the graph of the given function is concave up and concave down #f(x)= sinx-cosx# for #0<=x<=2pi#?
- What are the inflection points for #f(x) = -x^4-9x^3+2x+4#?

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